Okay, and that integral is the sum of the residues at x= 1 and x= -1. Have you found them? After you know the value of the contour integral, look at the circles on the ends. What is the limit of those integrals as the radius goes to 0? If you subtract that off, what is left is the integrals along the lines- that may be a problem because you are integrating from -1 to 1 and from 1 to -1.