Can Riemann Sums Be Negative?

Riemann sums may contain negative values (below the x‐axis) as well as positive values (above the x‐axis), and zero. Let f be a function defined on a closed interval [a, b].

Can an area be negative?

If ALL of the area within the interval exists below the x-axis yet above the curve then the result is negative . If MORE of the area within the interval exists below the x-axis and above the curve than above the x-axis and below the curve then the result is negative .

Is left Riemann sum underestimate?

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.