The value of the following complex integral, with $C$ representing the unit circle centered at origin in the counterclockwise sense, is:
$\displaystyle{}\int_{C}\frac{z^{2}+1}{z^{2}-2z}dz$
1. $8\pi i$
2. $-8\pi i$
3. $-\pi i$
4. $\pi i$