I was thinking about the problem that says:
Let $f: ~\mathbb R\rightarrow \mathbb R$ be a continuous function such that $\int_{-1}^{x}f(t)dt=0$ for all $x \in [-1,1]$. Then which of the following option(s) is/are correct?
(A) $f$ is identically $0$,
(B) $f$ is a non-zero odd function,
(C) $f$ is a non-zero even function,
(D) $f$ is a non-zero periodic function.
Please help. Thank you in advance for your time.