Simple contour integral with a parameter gone wrong

Question

I run into the following problem, I tried to evaluate a very simple integral:

Assuming[ a > 0  , Integrate[Sin[a*s]/(s - I)^2, {s, -Infinity, Infinity}]]

Mathematica claims the answer is zero, even though you can evaluate it by hand using residues to convince yourself that the answer is:

$I\ a\ \pi\ e^{-a}$

What is weird, is that if you substitute some numerical value instead of a the answer is correct. Also if you switch the pole to be +I Mathematica gives an incorrect answer:

$-2\ I\ a\ \pi\cosh(a)$

instead of simply minus the previous result. Anyone had a problem like this?