It does depend on it.If so, how come the answer doesnt depend on ? Does it not matter what the radius of the circle is?
Because the pole z=1 is within the circle, you get the result.
If it wasn't (say you considered as the circle of center 5 and radius 1), then the integral would have been 0.
Look here : Cauchy's integral formula - Wikipedia, the free encyclopedia (they say 'Then for every a in the interior of D')