Principal-valued integral over convex hull

squidsoft

Calculate without using the Residue Theorem:

[tex]P.V.\mathop\oint\limits_{z=H}\frac{1}{(z-1)(z+1)(z-i)}dz[/tex]

where [tex]H[/tex] is the straight-line segments connecting the poles. Can you generalize it to any polynomial [tex]P_n(z)[/tex] with distinct roots and the closed contour is over any sub-set of the zeros with again, straight-line segments connecting them?