Definition: The area of the region that lies under the graph of the continuous function is the limit of the sum of the areas of approximating rectangles (a) Use the above definition to determine which of the following expressions represents the area under the graph of from to .

(b) Evaluate the limit that is the correct answer to part (a). You may find the following formula for the sum of cubes helpful:

The value of the limit is .

You can earn partial credit on this problem.