Given $ S_t = S_0 + \mu + \sigma W_t $,
I am interested in finding the covariance $ Cov(S_t - S_0, S_T - S_t) $
The formula I am using is $ Cov(x, y) = E(xy) - E(x)E(y)$, having already calculated $ E(S_t - S_0)$ and $ E(S_T - S_t)$
Calculating $E[(S_t - S_0)(S_T - S_t)]$ leads to $ E[S_tS_T - S_t^2 - S_0S_T + S_0S_t ]$
Now, I, could try and separate these variables (although I am not sure about the $E[S_t^2]$, however this seems like a too complicated approach for this exercise, and was wondering if there is something I am missing with my approach so far?