On a given interval, if the antiderivative of f exists, is it unique? Why or why not? (You may cite theorems to support your answer.)

Question

The question basically asks for a specific given interval, if the antiderivative of f exists, is it unique?

If yes, why?

If no, why not?

In stating the reasons you can use specific theorems that would help support your answer.

Answer 1

The antiderivative is unique up to a constant.

If F(x)=∫f(x) dx and G(x)=∫f(x) dx, then F'(x)-G'(x)=0 which implies that F(x)=G(x)+C,