CALCULATING stochastic integral

Question

How can I calculate the stochastic integral $I_T (X)$ for all $T ∈ [0, ∞)$ of the stochastic process $$X_T = 5 × 1_{[0,3]} + \sin(W_2) × 1_{(3,7]} + \cos(W_7) × 1_{(7,8]}?$$

Here $W_2$ and $W_7$ are the values of Wiener Processes at $T=2$ and $T=7$, respectively.

Anyone help? Thanks.

Answer 1

The expression for $X_t$ is correct? It doesn't depend on $t$.