Principal-valued integral over convex hull

Calculate without using the Residue Theorem:

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

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