proving a statement about average value of a function over a region and a periodic function

Question

Let's say I've a function $f:[0,\infty]\to\mathbb{R}$ and it is periodic with $T$. If we take a look at the average value of this function over the hole region we can write:

$$\lim_{n\to\infty}\frac{1}{n}\int_0^nf(x)dx=\frac{1}{T}\int_0^Tf(x)dx$$

But how can prove that that is indeed true?