Sketch the vector field $F=($:$\frac{x}{\sqrt[\phantom{2}]{x^2+y^2}},\frac{y}{\sqrt[\phantom{2}]{x^2+y^2}}$:$)($or equivalently, $F=\frac{x}{\sqrt[\phantom{2}]{x^2+y^2}}i+\frac{y}{\sqrt[\phantom{2}]{x^2+y^2}}j).$

Integrate $f(x,y,z)=x-3y^2+z$ over the union of line segments $C_1$ and $C_2,$ where $C_1$ is the line segmen from $(0,0,0)$ to $(1,1,0),$ and $C_2$ is the line segment from $(1,1,0)$ to $(1,1,1).$