Dividing [0,2] into 4 sub-intervals gives us sub-intervals of length 0.5 and midpoints 0.25, 0.75, 1.25, 1.75 Since the distributive property says that *f* (0.25)(0.5) + *f* (0.75)(0.5) + *f* (1.25)(0.5) + *f* (1.75)(0.5)
and [*f* (.25) + *f* (0.75) + *f* (1.25) + *f* (1.75)](0.5) are the same thing, we can evaluate the one that only requires multiplying by 0.5 once: |