Please help me to answer the question below in detail. I really don't understand it. This's all the information I got for the question.Thank you so much, and have a great day!

3. Let p ( Pn. Define T(p) (x) = fo p(t)dt. (a) Is T a linear transformation? (b) What's the domain and range of T? (c) Determine Nul(T). (d) Determine the rank and nullity of T. (e) Let S be the standard isomorphism from Pr to R"+. Find a matrix A so that S- A(S(p)) = T(p). (f) Is the matrix A that you found in part (e) invertible? If so, find A-1. (g) What sources did you use for this exercise