Some identities for the Riemann zeta-function

Several identities for the Riemann zeta-function $\zeta (s)$ are proved. For example, if $s=\sigma +it$ and $\sigma >0$, then $${\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}\mathrm{\mid }\frac{(1-2^{1-s})\zeta (s)}{s}{\mathrm{\mid }}^{2}dt=\frac{\pi }{\sigma }(1-2^{1-2\sigma })\zeta (2\sigma )\mathrm{.}$$