Im attempting to show that the following isnottrue by cauchy's integral theorem.

$\displaystyle \int_{C}\frac{\overline{z}}{z^{2} - 5z - 6},dz = 0 $ where $\displaystyle C $ is the unit circle (travelled anti-clockwise).

Resolving $\displaystyle z^{2} - 5z - 6 = 0 $ i got z = 2 and z = 3 but these singularities lie outside the unit circle...

I know i need to do something with the $\displaystyle \overline{z} $ but cant figure out what