Line integrals and Green's theorem...

$($a$)$ Find a parameterization vec$(r{)}_1(t)$ of half of the circle radius $1,$ centered at $(1,0),$ going from $(2,0)$ to $(0,0)$ in a counterclockwise fashion. Hint: for general ellipses in standard orientation, a valid parameterization looks like $($:$x_0+$acos$(t),y_0+$bsin$(t)$:$).$

$($b$)$ For the vector field vec$(F)(y)=($:$y,1-y^2$:$),$ calculate ${\displaystyle \underset{C}{\overset{\phantom{}}{}}}$vec$(F)*dvec(r{)}_1.$

$($c$)$ Find a parameterization vec$(r_2)(t)$ of a line segment going from $(0,0)$ to $(2,0).$

$($d$)$ Once again calculate ${\displaystyle \underset{C}{\overset{\phantom{}}{}}}$vec$(F)*dvec(r_2).$

$($e$)$ Make a small sketch of the oriented path which combines parts $($a$)$ and $($c$).$ Apply Green's Theoren and compare the result with the sum of the line integrals.