I want to prove:
For an integrable function $f(x)$ and periodic with period $T$, for every $a \in \mathbb{R}$, $\int_{0}^{T}f(x)\;dx=\int_{a}^{a+T}f(x)\;dx.$
I tried to change the values and define $y=a+x$ so that $dy=dx$ and the limits of the integrals are as we want, but I'm not sure how to use the fact that $f(x)$ is periodic.
Thanks a lot!