Definite Integration

A particle moves along a line with velocity $v(t) = t^3 - t$ m/s for $t$ in $[-1,2]$. Find the total distance traveled by the particle during this time interval.

Find the total area bounded by the curve $y = x^3 - 3x$ and the $x$-axis from $x = -2$ to $x = 2$.

Find the area of the region bounded by the curves $y = x^2$ and $y = 2^x$ in the first quadrant.