Problem with a contour integral

[orion141]

I was w=kind of confused as of how to go about solving this integeal using complex methods. it is the Integral from 0 to infinity of{dx((x^2)(Sin[xr])}/[((x^2)+(m^2))x*r] where m and r are real variables. I tried to choose a half "donut" in the upper part of the plane with radii or p and R. Then I tried to break up the contour integral into paths 1, 2, 3, 4. is this the correct way to go about this? Thanks

 

[orion141]

I think that i figured it out... I found the residue at (im) as this is the only residue that contributes to the integral (-im is not in the contour and R(0)=0). Does this sound right? Thanks