Evaluate the contour integral: $$ I = \int_{C_0} \frac{dz}{z^2+z} $$ where the curve $C_0$ in the complex plane is given by: $$ C_0 = \{z : |z| = 1 \text{ and } z \neq -1\}$$ and the integral is taken in the counterclockwise direction on the curve.
I thought about using residue theorem to evaluate this, but I wasn't sure if the fact that the region we are integrating around isn't closed (since we are not including -1) will mean that I can't use residue theorem.