Using Cauchy's integral formula calculate

$$

\int_\Gamma \frac{dz}{z^2-2z+10},

$$

where $\Gamma$ is a counter-clockwise oriented simple contour, not passing through eiter

of $1\pm 3i$ in the following cases

**(a)** The point $1+3i$ is inside $\Gamma$ and $1-3i$ is outside it;

**(b)** The point $1-3i$ is inside $\Gamma$ and $1+3i$ is outside it;

**(c)** Both points $1\pm 3i$ are inside $\Gamma$.