Just a little confused about the following. Given that $\displaystyle W$ denotes a one-dimensional standard Brownian motion, find $\displaystyle Cov(W_t,W_s)$

Step 1: Assume that $\displaystyle s \leq t$, then

$\displaystyle Cov(W_t,W_s)=E[W_tW_s]=E[(W_t-W_s+W_s)W_s]=Var(W_s)=s$

Step 2: Then, in general:

$\displaystyle Cov(W_t,W_s)=\min \{s,t\}$

Could someone explain each step and properties used? Thanks.