May the force (field) be with you

Calculus Level 3

What is the amount of work done by the particle moving in the force field $F(x,y) = x^2\ \mathbf{i} + xy\ \mathbf{j}$ along the quartile circle $r(t) = \cos t\ \mathbf{i} + \sin t\ \mathbf{j}$ from $t=0$ to $t = \frac{ \pi}{2}$ ?

Details and assumptions

Work done can be calculated using the formula $W = \int_C F\cdot dr$ .