I have an argument where, with a meromorphic function $\phi$ satisfying $\phi(s) = \phi(1-s)$, the following equality appears: $$\int_{(2)} \phi(s) y^{-s} \, ds = \int_{(1/2)} \phi(s) y^{-s} \, ds$$
where the integration domains are the vertical lines of real part fixed to $2$ and $1/2$ respectively. For me a change of variables would give a relation between integrals on $(2)$ and $(-1)$, because these are symmetric with respect to $s \mapsto 1-s$, however I do not understand why the equality above is true.
Is there any standard trick I should see to prove it?