Show that a standard Brownian motion $\displaystyle \{W_t\}_{t \geq 0}$ is a martingale with respect to the filtration $\displaystyle \{F_t \}_{t \geq 0}$, where $\displaystyle F_t = \sigma(W_s : 0 \leq s \leq t)$. Moreover, show that $\displaystyle \{ W_t^2 + t \}_{t \geq 0}$ is a martingale with respect to the filtration $\displaystyle \{F_t \}_{t \geq 0}$.

First part I have done, but for the second part I arrive at a point where I have this...

$\displaystyle \mathbb{E}[(W_t - W_s)^2]$

which is apparently equal to $\displaystyle t-s$. Why is this?

(More info if needed)

$\displaystyle \mathbb{E}[(W_t^2 - t |F_s] = \mathbb{E}[(W_t - W_s + W_s)^2 - t|F_s]$ and continuing I arrive at the above result I'm stuck at.