21. The region S is bounded by y = x² – 2x + 3, y = 0, x = 0, and x = 9. Which of the following is the approximation to the area of S obtained by computing the sum of the areas of the 3 inscribed rectangles with bases [0,3], [3,6], and [6,9] (lower Riemann sum)?

The parabola y = x² – 2x + 3 has a minimum of y = 2 at x = 1 (see the graph below). Thus the three inscribed rectangles have heights of 2, 6, and 27 respectively. Since each has a base of length 3 the Riemann sum has the value (2+6+27)3 = 105.