Questions $7-9$ concern the vector field

$F(x,y,z)=y^{2}zi+xzj+xyk$

and the curve $C$ consisting of the straight line segments joining $(1,0,0),(1,1,0),(1,1,1),$ and $(1,0,1),$ shown below:

Using an appropriate integral theorem or otherwise, calculate the line integral $o{\displaystyle \underset{F}{\overset{\phantom{}}{}}}*dr.$

The vector field $F(x,y,z)$ is conservative.

$$ True

False