WORK ALONG DIFFERENT PATHS Find the work done by $F=(x^2+y)i+(y^2+x)j+z^{z}k$ over the following paths from $(1,0,0)$ to $(1,0,1).$

a$.$ The line segment $x=1,y=0,0z1$

b$.$ The helix $r(t)=(cost)i+(sint)j+(\frac{t}{2})k,0t2$

c$.$ The $x-$axis from $(1,0,0)$ to $(0,0,0)$ followed by the parabola $z=x^2,y=0$ from $(0,0,0)$ to $(1,0,1)$