I faced the problem that says:
If $f\colon \mathbb R \rightarrow \mathbb R$ is a continuous function and $f(x)=\int_0^xf(y)~dy.$ Then which of the following option is correct?
$3.f$ is identically $0$
$4.f$ is identically $1$.
My attempt: Here,$f'(x)=f(x)$ and so finally we can come $f(x)=Ae^x, A$ being a constant.So,option $1$ looks right.Am I right? Thanks in advance for your time.