Power of periodic signal Given a signal
$s(t) = e^{j(t+\pi)}$,
I conclude that the signal is periodic with period $T=2\pi$, so its power should be
$$P = \frac{1}{T}\int_{-T/2}^{T/2}|s(t)|^2dt= \frac{1}{2\pi}\int_{-\pi}^{\pi}|1|^2dt = \frac{1}{2\pi}t|^{\pi}_{-\pi}=\frac{\pi-(-\pi)}{2\pi}=1$$

Is the formula for the power of a periodic signal correct?
The average power of a signal $s(t)$ is given by

$$\overline{s^2(t)}=\lim_{T\rightarrow\infty}\frac{1}{T}\int_{-T/2}^{T/2}|s(t)|^2dt\tag{1}$$

If $s(t)$ is periodic, $(1)$ is equivalent to the average power in one period:

$$\overline{s^2(t)}=\frac{1}{T}\int_{-T/2}^{T/2}|s(t)|^2dt\tag{2}$$

where $T$ now denotes the period of $s(t)$.