When Is a Riemann Sum an Overestimate?

If the graph is increasing on the interval, then the left-sum is an underestimate of the actual value and the right-sum is an overestimate. If the curve is decreasing then the right-sums are underestimates and the left-sums are overestimates.

Are Riemann sums accurate?

Riemann sums sometimes overestimate and other times underestimate. Riemann sums are approximations of the area under a curve, so they will almost always be slightly more than the actual area (an overestimation) or slightly less than the actual area (an underestimation).

How do you know if approximation is over or underestimate?

If the graph is concave down (second derivative is negative), the line will lie above the graph and the approximation is an overestimate.