$M_t=\exp{(\sigma B_t-\frac{\sigma^2}{2}t)}$ is the exponential martingale. $A_t=\int_0^tM_sds$ is the time integral of $M_s$. The question is calculate the $E(A_t)$ and $Var(A_t)$.
I get that $E(A_t)=\int_0^t E(M_s)ds=t$.
$Var(A_t)=E(A^2_t)-(E(A_t))^2$
$E(A^2_t)=.....$
Is this the right way or any other solutions?