x\;\text{versus}\;y
For the function \boxed{f(x)=\frac{2z^2+2}{x^2-3z}}\sin x^2, identify the poles (singular points), find the corresponding residues, and evaluate the integral
I=\oint_C f(z)dz \text{,}
\sum_x^y \sin \theta
where C is the contour \lvert z\rvert=5, mapped counter-clockwise.