> 
> Suppose $f:\mathbb{R}\to\mathbb{R}$ is a continuous function. If for any bounded interval $[a,b]\subset\mathbb{R}$ we have
>  $$\Bigg|\int^b\_af(x) dx \Bigg|\le(b-a)^2$$
>  Prove that $f(x)=0$ for all $x \in \mathbb{R}$.
> 
> 
> 

I've been looking at this statement for a few hours. It seems very simple but I can't really see a good place to start. Can someone point me in the right direction?