Let $Z_t=\int{W_s }ds $. Show that $Z_t=\int (t-s) dW_s$

Question

Let $Z_t=\int_{0}^{t} W_s ds$. Use integration by parts to show that $Z_t=\int_{0}^{t} (t-s) dW_s$. I have tried and i can't get the answer.

Answer 1

Note that \begin{align*} d(sW_s) = sdW_s + W_s ds. \end{align*} Then you can integrate on both sides.