Let $f$ be differentiable everywhere. Suppose $f$ and $f^{\prime}$ are Lebesgue integrable. Show that $f(x)\to 0$ when $x\to \infty$.

Question

Let $f$ be differentiable everywhere. Suppose $f$ and $f^{\prime}$ are Lebesgue integrable. Show that $f(x)\to 0$ when $x\to \infty$.

Could I get some hints on how this could be done?