a$)$ Approximate the area under $f(x)=x^3-3x^2-x+7$ and above the $x-$axis on $-1,3$ with dots

$($i$),$dotsn$=8$ rectangles using the left endpoint.

$($ii$)$ dotsn$=8$ rectangles using the right endpoint.

$($iii$)$ dotsn$=8$ rectangles using the Trapezoidal Rule.

$($iv$)$ dotsn$=4$ rectangles using the midpoint.

b$)$ Write the definite integral that would represent the actual area and evaluate it$.$