Evaluate ${\displaystyle \underset{-2}{\overset{3}{}}}(x^2-3)dx$

Evaluate ${\displaystyle \underset{-2}{\overset{0}{}}}(\frac{1}{2}{t}^4+\frac{1}{4}{t}^3-t)dt$

The velocity function $($in meters per second$)$ is given for a particle moving along a line.

$($a$)$ Find the displacement

$($b$)$ Find the distance traveled by the particle during the given time interval.

$v(t)=3t-5,0t3$

$2$