expectation of stochastic integral

I am trying to figure out how to calculate E[I B^2 dB] and E[(I B dB)^2]

where B is a standard brownian motion, and I have used I to denote the integral between 0 and t.

I can only think that I must maybe show that the integrals are martingales, but this is probably not correct..

Does anybody have any idea how I can calculate these expected values???