Hello! If I have a real integral between ##-\infty## and ##+\infty## and the function to be integrated is holomorphic in the whole complex plane except for a finite number of points on the real line does it matter how I make the path around the poles on the real line? I.e. if I integrate on the semicircle in the upper plane and I have a pole at 0 let's say, do I get the same result if I go around the pole above or below the real axis? Thank you!