Answer the following step by step and explanation included

1. a. Using the definition of the definite integral, express the area bounded by f(x) = x 3 + 3, y = 3 and x = 1 as a limit.

b. Using the fact that Xn i=1 i 3 = 1 4 n 2 (n + 1)2 , compute the limit obtained in part a

Using the fact that :1"? = imam + 1)2, compute the limit obtained in part i=1