Use upper and lower sums to approximate the area of the region using the given number of subintervals (of equal width). y=`sqrt(x)` +5 Find the...

The upper sum
and lower sum refer to the sums of areas of the rectangles resulting from breaking up the
interval into smaller segments.

The lower sum is the sum
of the areas of rectangles UNDER the curve (thus, this approximation will be slightly smaller
than the actual area under the curve.) In this case, the first rectangle has vertices

(0,0), (0.25, 0), (0, 5) and (0.25, 5). The area of this rectangle is 0.25*5 =
1.25

The second rectangle is next to the first one and has vertices

(0.25, 0), (0.5, 0), (0.25, 5.5) and (0.5, 5.5). (5.5 is the value of the function y =
f(0.25)). The area of this rectangle is 0.25*5.5 = 1.375

As you can see, the
area...