inverse fourier transform application:

So the question states:

apply the inverse fourier transform to your answer to the previous problem to show that for x>0 and a> 0,

integral (0 to infinity) ((s sin sx) / (a^2+s^2)) ds = (pi/2) e^(-ax).

So the previous problem was:

Find the fourier transform of the function f defined by:

f(x) = -e^(ax) x<0

= e^(-ax) x>0

and my answer for the x>0 part was: 1/(a+ik)

so applying the inverse fourier transform to the f(x) = e^(-ax) bit,

f(x) = 1/2pi . integral (k=-infinity to infinity) f hat (k) e^(ikx) dk

sooooo get:

f(x) = 1/2pi . integral (k=-infinity to infinity) 1/(a+ik) e^(ikx) dk

and i have no idea where to go from here, please help!