Martingale representation of European option

Let stock price $$S$$ satisfy

$$S(t)=S(0)e^{(\int_0^t\sigma(s)dB_s-\frac{1}{2}\int_0^t\sigma(s)^2ds)}$$

I want to calculate the Martingale representation $$V(t)=E(F|F_t)$$ of European option with strike price $$M$$ and maturity $$T$$ which is given by

$$F=(S(T)-M)^+$$

How to find the solution and the Black-Scholes PDE?