Suppose $f(z)$ is a analytic function inside and on the contour $m=1$, by using Residue Theorem, $\int_{m=\rho}\frac{f(z)}{z1}dz=2\pi f(1)$ for any $\rho>1$, but how to calculate the integration $\int_{m=1}\frac{f(z)}{z1}dz$? It seems that the answer is $\pi f(1)$, but how to prove it. Are there any reference?

See http://en.wikipedia.org/wiki/Cauchy_principal_value and http://www.damtp.cam.ac.uk/user/stcs/courses/fcm/handouts/cauchy_principal_value.pdf. 

