$$f(x)=\int_0^x(t-1)(t-3)\,\mathrm dt$$
This question is written under Rolle's theorem, which makes me pretty confused as I thought of using the second part of the fundamental theorem of calculus. However, I am not sure how to apply either theorem , whichever is the correct one, in order to find the critical points.
I know that the critical points are were the function is $0$ or undefined (yes, according to my book, critical points are also where the function is undefined).
I suppose that$$f(x)=\int_0^x(t-1)(t-3)\,\mathrm dt.$$Then the critical points are the points where $f$ is undefined (I guess that there are none) and those such that $f'(x)=0$. That means that the critical points are $1$ and $3$, since $f'(x)=(x-1)(x-3)$.