Let $B$ be a standard Brownian motion and $ W_t=(1-t)\int_0^t \frac{1}{1-s}dB_s $ be a Brownian bridge.
Calculate $dW_t$.
To apply Ito formula define $ f(t,B_t)=(1-t) \int_0^t\frac{1}{1-s}dB_s $ Then \begin{align} f_t(t,B_t)&=-\int_0^t\frac{1}{1-s}dB_s+(?) \\ f_{B_t}(t,B_t)&=(?) \\ f_{B_t,B_t}(t,B_t)&=(?) \end{align}
What are the (?) and how do we get them?