(2) Let's develop a "sequential" version of integrability for a bounded function defined on a closed interval A = [a, b]. (a) Prove that there exists a sequence { Pn} of partitions of A so that L( f, Pn) - L(f) and U(f, Pn) - U(f). (b) Prove that f is integrable on [a, b] if and only if there exists a sequence { Pn} so that (U(f, Pn) - L(f, Pn)) + 0. (c) Prove that in both (a) and (b), we may choose the sequence { Pn} so that mesh(Pn) + 0. (Here, "mesh(Pn)" refers to the maximum of lengths Ax; of the subintervals of the partition Pn.)