$\Gamma$ refers to a once continuous counterclockwise closed circle with center $\xi =2$ and with a positive radius $r=3$. I need to determine the following integral $\frac{1}{z+2}$.

Why is $\int\_{\Gamma } f \left ( z \right )dz=0?$

I know that is something connected with holomorphic function and line integral but still can't find the rules how to calculate integral of function when I have specific value of radius and center?

If someone could help me, I would be really thankful.