How Do Contour Integrals Apply to Green's Functions in Acoustic Wave Equations?

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A question about an integral encountered in a paper I am reading about Green's Functions of the acoustic wave equation ...

The integral encountered:

Im{Integrate[ exp((i*y-a)*k), dk, 0, Infinity]} = Re{1/(y+ i*a)}

where i = sqrt(-1) and a,y,k elements of R. Been a while since I've calculated residues and what not, not sure if that is even the right procedure. Any help with how to calculate the integral?
 
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laplace transform

The solution involves Laplace transforms. Closed.
 

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