Integrate (z^2 - 4)/(z^2 + 4) counterclockwise around the circle |z - i| = 2.

Here's my attempt.

|z - i| = 2

|z - 2| = i

z0 = 2

(z^2 - 4)/(z^2 + 4)

= ((z + 2)(z - 2))/(z^2 + 4)

= (z + 2)/(z^2 + 4) * i

f(z) = (z + 2)/(z^2 + 4)

2i*pi*f(z0) = 2i*pi*(1/2) = i*pi

The answer is -4*pi. Please tell me what I'm doing wrong.