Integral of a periodic function

Question

If $F:\Bbb R\to \Bbb C$ is $2\pi$-periodic and Riemann integrable on $[-\pi, \pi]$, then show that for all $\alpha\in \Bbb R$, $$\int _{-\pi}^{\pi} F(t)dt=\int_{\alpha-\pi}^{\alpha+\pi} F(t)dt.$$