Let $f \in \mathcal { C } ^ { 0 } ( [ 0 , + \infty [ )$ and $\ell \in \mathbb { R }$. Prove that
$$\left( \lim _ { x \rightarrow + \infty } f ( x ) = \ell \right) \Rightarrow \left( \lim _ { x \rightarrow + \infty } \frac { 1 } { x } \int _ { 0 } ^ { x } f ( t ) d t = \ell \right)$$