Question

She said,"I shall use a backrest when i travel next time."indirect speech.

Answer 1

Answer:

She said that she would use a backrest when she travelled next time.

Explanation:

You could even drop "that" from the sentence. It is still acceptable.

Answer 2

Actually the correct one is

She said that she should use a backrest when she travels next time

Explanation

because shall will convert to should