CaptainBlack addressed (a)

for (b): i told you how to find a potential function $\displaystyle f(x,y,z)$ before. i gave you a full solution to one of your problems

here. please review it

for (c): recall the fundamental theorem for line integrals.

if $\displaystyle C$ is a smooth curve given by the vector function $\displaystyle \bold{r}(t)$ for $\displaystyle a \le t \le b$, and $\displaystyle f$ is a continuous function whose gradient vector $\displaystyle \nabla f$ is continuous on $\displaystyle C$, then

$\displaystyle \int_C \nabla f \cdot d \bold{r} = f(\bold{r}(b)) - f(\bold{r}(a))$

note here that your $\displaystyle \bold{F} = \nabla f$ that is mentioned