2015 Q&A Bank 2.13 (iii) If the question is asking for the expected value at u, why does the solution integrate from u to t? Are we not only concerned with 0 to u?
The limits of the integral are given in the question, that's why we need to integrate between 0 and t in the solution. It turns out that we really are only interested in the portion between 0 and u because the expected value of the integral between u and t is zero.