$$X_T = x_t+\int_t^T\mu(s,X_s)ds+\int_t^T\sigma(s,X_s)dW_s$$ where $W$ is a Wiener process. What is the variance and mean of this process?
It is well known $$E\left[\int_t^T\sigma(s,X_s)dW_s\right]=0.$$ But I haven't found formulas for the rest. So, what is the general formulas for: $$ E\left[\int_t^T\mu(s,X_s)ds\right] \text{, } \text{var}\left[\int_t^T\mu(s,X_s)ds\right] \text{ and } \text{var}\left[ \int_t^T\sigma(s,X_s)dW_s\right].$$ If $\mu$ and $\sigma$ is in linear in $X$ then the process is a Geometric BM and the distribution is known but what if they are not linear
