Let $F=($:$-y^2,xy$:$),$ and let $C$ be the upper half of the unit circle, oriented from $(1,0)$ to $(-1,0).($Note that $C$ is not a closed curve.$)$ Calculate ${\displaystyle \underset{C}{\overset{\phantom{}}{}}}F*ds.$

Let $F=($:$-\frac{y}{2},\frac{x}{2}$:$),$ and let $C$ be the curve shown below. What is $o{\displaystyle \underset{C}{\overset{\phantom{}}{}}}F*ds?$ Explain