Given a line L that goes from $\displaystyle l-\infty i $ to $\displaystyle l+\infty i $ and a line C that goes from $\displaystyle c+\infty i $ to $\displaystyle c-\infty i $, $\displaystyle l \neq c, \; l,c > 0 $, and a function $\displaystyle f(z) $ such that $\displaystyle f(z) $ is analytic everywhere in the strip aside from one pole inside the strip. Call the residue at that point $\displaystyle S $.

Is it true that $\displaystyle \int_{L} f(s)ds + \int_{C} f(s)ds = 2\pi i S $ ?