The domain of $f(x,y)$ is the $xy$-plane, and values of $f$ are given in the table below.

Find $\int_C \mbox{grad } f\cdot d\vec{r}$, where $C$ is

(a) A line from $(0,4)$ to $(2,1)$.
$\int_C \mbox{grad } f\cdot d\vec{r} =$

(b) A circle of radius $1$ centered at $(1,3)$ traversed counterclockwise.
$\int_C \mbox{grad } f\cdot d\vec{r} =$