Suppose $\vec{F}(x,y) = x^2 \vec{i} + y^2 \vec{j}$ and $C$ is the line segment segment from point $P = \left(-3,1\right)$ to $Q = \left(-6,4\right)$.

(a) Find a vector parametric equation $\vec{r}(t)$ for the line segment $C$ so that points $P$ and $Q$ correspond to $t = 0$ and $t = 1$, respectively.
$\vec{r}(t) =$

(b) Using the parametrization in part (a), the line integral of $\vec{F}$ along $C$ is
$\displaystyle \int_C \vec{F} \cdot d \vec{r} = \int_a^b \vec{F}(\vec{r}(t)) \cdot \vec{r}\,'(t) \, dt = \int_a^b$ $dt$
with limits of integration $a =$ and $b =$

(c) Evaluate the line integral in part (b).