Urgent, residue and winding numbers

1. Evaluate the integrals

$\displaystyle \int ^{2\pi} _0 \frac{dt}{2+sint}$

and

$\displaystyle \int ^{\infty} _0 \frac{x^2}{x^4 +x}dx$

2. Let $\displaystyle z_1,z_2,z_3,z_4 \epsilon \mathbb{C}$ be the vertices of a closed quadrilateral $\displaystyle \Box$ such that $\displaystyle [z_1,z_2] \oplus [z_2,z_3]\oplus [z_3,z_4]\oplus [z_4,z_1]$ traverses $\displaystyle \partial \Box$ in counterclockwise direction (abusing notation, we shall write $\displaystyle \partial \Box$ for that curve) show that $\displaystyle v(\partial \Box,z)$ is 0 for $\displaystyle z\epsilon \mathbb{C} ` \Box$ (C-minus Box) and 1 if $\displaystyle z$ is an interior point of $\displaystyle \Box$ (Hint: do not attempt to parametrize $\displaystyle \partial \Box$..)