How to prove that the following process is a Martingale using Ito's formula?

Question

I am asked to prove that $Y_t$ is a martingale where $Y_t=\exp\left(\int_0^tf(s)\,dW_s-1/2\int_0^tf(s)^2\,dt\right)$ using Ito's formula.

After applying Ito's formula (I hope I made no mistake) I get $dY_t= Y_t \, dM_t$ where $M_t=\int_0^tf(s) \, dW_s$

What to do next ?

Answer 1

Maye does this work : We have $Y_t=\int_0^tY_sf(s)dW_s$ where W is a brownian motion, so $Y_t$ is a Wiener(ito) integral and thus it is a martingale