In the study of the free region of zeros of the Riemann $\zeta$ function I'd like to know if this form is correct, where s is the complex variable $s=\sigma+ it$
$\int_{\sigma_1, t_1}^{\sigma_{2},t_2} \zeta'(s) ds = \zeta(\sigma_2,t_2) - \zeta(\sigma_1,t_1)$?
or if t is constant $\int_{\sigma_1, t}^{\sigma_{2},t} \zeta'(s) ds = \zeta(\sigma_2,t) - \zeta(\sigma_1,t)$?