contour integration

Consider the line integral $I = \int_C (x^2 +iy^2)dz$, where $z = x + iy$. The line $C$ is shown in the figure below. The value of $I$ is

$$\oint {{{{z^2} - 4} \over {{z^2} + 4}}} dz\,\,$$ evaluated anticlockwise around the circular $$\left| {z - i} \right| = 2,$$ where $$i = \sqrt { - 1} $$, is

Given $$f\left( z \right) = {1 \over {z + 1}} - {2 \over {z + 3}}.$$ If $$C$$ is a counterclockwise path in the $$z$$-plane such that $$\left| {z + 1} \right| = 1,$$ the value of $...