I have to caluclate the following expressions, can sb verify my results, please?
$$E\left(\int_0^2W_t \, dt \mid F_1\right)$$
My result: $\displaystyle\int_0^1W_t \, dt + \frac{5}{2} +W_1$ (corrected)
$$E\left(\int_0^2(4t^2+t) \, dW_t+\int_0^1t^2 \, dt\right)$$
My result: $\dfrac{1}{3}$
$$D^2\left(\int_0^1(t^2+1)\,dW_t\right)$$
My result: $\dfrac{28}{15}$