Answer
$\left\langle \frac{212}{3}, 124 \right\rangle.$
Work Step by Step
We have
\begin{align}
\int_{-1}^{3}\left\langle 8 t^{2}-t, 6 t^{3}+t\right\rangle d t&=\left\langle \frac{8}{3} t^{3}-\frac{1}{2}t^2, \frac{6}{4} t^{4}+\frac{1}{2}t^2\right\rangle|_{-1}^{3}\\
&=\left\langle 72-\frac{9}{2}, \frac{243}{2} +\frac{9}{2}\right\rangle-\left\langle -\frac{8}{3} -\frac{1}{2}, \frac{6}{4} +\frac{1}{2} \right\rangle\\
&= \left\langle \frac{212}{3}, 124 \right\rangle.
\end{align}
