How can one calculate stochastic differential of the following process?
$$Y_t = \exp \left(t^2+\int_0^ts \, \mathrm d W_s\right)$$
There are two approaches, which one is correct? Both?
$Z_t=t^2+\int_0^ts \, dW_s$ is an Ito process, so just apply Ito formula with respect to $Z_t$ to the function $f(Z_t)=e^{Z_t}$
Apply Ito formula with respect to $W_t$ and $t$ to the function $f(t,W_t)=e^{t^2+\int_0^ts \, dW_s}$
Here, $W_t$ is the standard Brownian motion (Wiener process). Thanks for any explanation.