Suppose a particle does a lap around the unit circle, starting and endir' at $(1,0),$ and subject to the force

$F=x^{2}i-y^{2}j$

Find the work done by the force along this path.

$0$

$-\frac{2}{3}$

$\frac{2}{3}$

$-\frac{1}{3}$

$\frac{1}{3}$