Let $f$ be integrable on $\mathbb{R}$. Prove that $$\lim_{h \rightarrow 0} \int \vert f(x+h)-f(x) \vert dx=0.$$
My question is I know since $f$ is integral can I use that for any $\epsilon > 0$, I can find a finite interval such that on the complement of this the ball we have
$$\int_{B^c} \vert f \vert dx < \epsilon.$$
Can I use this to prove my statement? And use some relationship between $\vert f(x+h)-f(x) \vert$ and $\vert f(x) \vert$? Just need hint. sorry if this has been asked I couldn't find it.
