(a) Use the definition given below with right endpoints to express the area under the curve y = x from 0 to 1 as a limit. The area A of the region S that is bounded above by the graph of a continuous function y = f(x), below by the x- axis, and on the sides by the lines x = a and x = b is the limit of the sum of the areas of approximating rectangles. n A = lim R = lim [f(x)Ax + f(x2) Ax + + f(x)Ax] = lim f(x;) Ax n 7-00 n i=1 lim (b) Use the following formula for the sum of cubes of the first n integers to evaluate the limit in part (a). 2 13+2333..+n n(n + 1) = 2