I know that $\int_0^t f(s)dW_s$ has normal distribution with variance $\int_0^t f(s)^2ds$ where $W_t$ - Wiener process and $f$ is deterministic function.
But what if we have also $t$ in function? Like $\int_0^t \sin{(t-s)}$?
IT also have normal distribution with variance $\int_0^t \sin^2{(t-s)}ds$? And it's always true?
So I if I have to find a distribution of $\int_0^t W_s \cos(t-s)ds$ I use integration by parts and I get $\int_0^t \sin(t-s) dW_s$ do it Has distribution as I write above?