will/would

will = simple future

would = Would is a past-tense form of will. If you are writing about past events, you can use it to indicate something that was in the future at that point in time, but is not necessarily in the future right now. In other words, you use would to preserve the future aspect when talking about the past.

(all this info is on google)

Could you please tell me the different in nuance between A and B by using your own words?

A. He said that he will go to Kyoto tomorrow.
This sentence expresses definiteness in him going to Kyoto tomorrow.
B. He said that he would go to Kyoto tomorrow.
This sentence expresses expectation, intent, desire, etc., in him going to Kyoto tomorrow.

Thank you for yor comment.

I would prefer to preserve the time relation

Present and simple future:
We can use the present if someone has said something in the immediate past or with relevance to the present - I have just asked him what he will do. He says he will go to Kyoto tomorrow.

Simple past and future-in-the-past:
I would use this about sayings in the more distant past:

I asked him last week what he would do. He said that he would go to Kyoto tomorrow.

I asked him last week what he would do. He said that he would go to Kyoto the next day.
In this contex , can I use "the nex day" ?

Sure, as long as the intent is still not definite. Would implies "maybe", might happen, might not, but he will try.

If you say: "I asked him last week what he would do. He said he will go Kyoto the next day" it implies that he is definitely going to Kyoto.

Thank you for your comment.

The usefulness is exactly as infra blue explained.
Preserving the time is not enough.
The first example intents at certainty while the second merely describes an intention that might not be valid anymore.

Thank you for your kindness.

You are confusing direct and reported speech. No native speaker would ever say that. It's 'he would'. In reported speech, the tense changes: "I will be in Geneva on Monday", he said. He said that he would be in Geneva on Monday.

See guidance here:

http://www.ef.co.uk/english-resources/english-grammar/tense-changes-when-using-reported-speech/

You would only use 'will' when quoting direct speech. Also time references e.g. tomorrow, next week etc are preserved. Thus your sentence might be altered thus:

Direct speech:
I asked him last week what he would do. He said "I will go to Kyoto tomorrow"

Reported speech:
I asked him last week what he would do. He said he would go to Kyoto the next day.

This is flat out false. At least within the realm of reported speech, which it is.

The change in tense we see in indirect reported speech has nothing to do with an actual change in tense reflecting a changed reality.

Bill: "I'm going to get pizza." [Bill leaves.]
Judy: Where's Bill?
Ann: He WENT to get pizza.

['went' here is a true past tense reflecting the changed reality, Bill is not here, he's "went".

Bill: I'm going to get pizza.
Judy [to Ann]: What did Bill say?
Ann: He said that he WAS going to get pizza.

WAS does not reflect a new reality. Bill hasn't gone yet. This WAS is only a backshift used by English speakers, Ann in this case, to reflect that she is not quoting Bill directly/perfectly/word for word, she is only telling the content of what he said.

Ann could say, [direct speech]

Ann: He said, "I'm going to get pizza."

Backshifting, as it is called, is only used to mark the distinction between Direct Reported Speech and Indirect Reported Speech.

A. He said that he will go to Kyoto tomorrow.

B. He said that he would go to Kyoto tomorrow.

Here, B. expresses as much definiteness as A. does. Native speakers don't always backshift, but regardless, the will and the would are identical in strength, identical in definiteness.

C, below, is also a possibility.

C He said that he is going to/going to go to Kyoto tomorrow.

In reported speech, the "tenses" do NOT have to change. It is a choice made by the speaker and there is no reason that there must/has to be a backshift.

In reported speech, the "tenses" do NOT have to change. It is a choice made by the speaker and there is no reason that there must/has to be a backshift.

Really, Punkey?

camlok: I will pick up the pencil.

[reaches over and picks up the pencil from the floor]

camlok: *I would pick up the pencil.* [*denotes ungrammatical for this specific purpose]