Rectangles by computer

You will write three ways of adding rectangles under a curve: with the right-hand corners, the left-hand corners and the middles of the strips. The checker compares them with known values.

The idea. Cut $[a, b]$ into $n$ strips of width $h = \dfrac{b - a}{n}$. The right-hand sum uses the heights $f(a + h), f(a + 2h), \dots, f(a + nh)$. The left-hand sum uses $f(a), f(a + h), \dots, f(a + (n - 1)h)$. The middle sum uses $f(a + (r + 0.5)h)$ for $r = 0, \dots, n - 1$. Each is multiplied by $h$.

Your tasks.

1. Finish right_sum(f, a, b, n).
2. Finish left_sum(f, a, b, n).
3. Finish middle_sum(f, a, b, n).