You changed the bound of the integral wrong hehe. When u=cosx, then your lower bound with respect to u is 1 and upper bound is zero. Always remember that $\int_{1}^{0} =-\int_{0}^{1}$ so you have to use a property of integral to make the lower bound 0 and upper bound 1, but you have to multiple the integral by -1. That will cancel out your negative and you will get 8/15.