Using Green's Theorem, the Line Integral $\int$ C $x ^ { 2 } y d x - y ^ { 2 } x d y$

Multiple Choice

Using Green's Theorem, the line integral $\int$ C $x ^ { 2 } y d x - y ^ { 2 } x d y$ where C is the circle $x ^ { 2 } + y ^ { 2 } = 1 \text {, }$ is

A) $\frac { \pi } { 3 }$
B) $\frac { \pi } { 4 }$
C) $- \frac { \pi } { 4 }$
D) $- \frac { \pi } { 3 }$
E) $- \frac { \pi } { 2 }$