Optimum point of $f(s) = \int_0^{\pi} \frac{ \exp(-s) y \cos(ky)}{s^2+y^2} \,dy $

Question

Is it possible to find optimum point for the following function f(s) (i.e. $df/ds=0$): $$ f(s) = s e^{-s} \int_0^{a} \frac{ y \cos(\frac{\pi}{a} y)}{s^2+y^2} \,dy $$ or $$ f(s) = s e^{-s} \int_0^{a/2} \frac{ y \cos(\frac{\pi}{a} y)}{s^2+y^2} \,dy $$