I still don't get why only one sample is sufficient. We assume we don't know c and d right?
I think the "only one sample" refers to the sample at the middle point of a and b. Then we could use the function value there to evaluate the integral.
The one sample here refers to the middle point, but in general I think, as long as the function is continuous along the integral domain, there is always a point on the curve that represents the average?