1. There are changes in the verb tenses of some modal verbs in Reported Speech:
will/shall would, can could (present) / would be able to (future), may might,shall should (asking for advice) or would(asking for information), must must / had to (obligation)(must remains the same when it expresses possibility or deduction).
2. Would, could, used to, mustn’t, should, ought to andhad better remain the same.