The question say: let $f$ be the Thomae function given below:
And let $g(x)= \int_{0}^{x} f(t)dt$. Prove that $g'(x) = f(x)$ iff $x \in \mathbb{Q}.$
I was told that the question contain a mistake, but I do not know what is it, could anyone tell me it please?
Instead of $x\in\mathbb Q$, it should be $x\in[0,1]\setminus\mathbb Q$. The function $g$ is the null function and therefore $g'$ is the null function too. And $f(x)=0$ if and only if $x\in[0,1]\setminus\mathbb Q$.