Method
Approximating \int_{0}^{2} f(x)\,dx with the left Riemann sum, n = 12. Drag the amber handles to move a and b.
f is increasing on [0, 2], so each left endpoint is the lowest point of its strip: every rectangle sits below the curve, and the left sum underestimates the integral.
Left sum (n = 12)
2.342593
exact (numerical)
2.666667
error
-0.324074
Riemann Sum Visualizer: Rectangles, Error, and Rules from CalcLearn, free AP Calculus study tools.