For example given an integral
$$ \int^t_0 \exp(aW(t'))\,dt', t\in\mathbb R_+ $$ where $W(t')$ is a standard Wiener process.
I've been very confused about stochastic integrals like $\int^t_0 W(t')\,dt'$, for example here Integral of Brownian motion w.r.t. time
My question is how to numerically simulate this integral (i.e. simulate trajectories with evolution of time)