numerical analysis...

I know this is late, but what you want to do is setup the following
$y' = f(t,y) \Rightarrow \int_{t_k}^{t_{k+1}}\! y' \, dt = \int_{t_k}^{t_{k+1}}\! f(t,y) \, dt \Rightarrow y_{k+1} = y_k + \int_{t_k}^{t_{k+1}}\! f(t,y) \, dt$

For Adams-Bashforth interpolate $f(t,y)$ at the points $t_{k-2}, t_{k-1}, t_{k}$ using the Lagrange interpolating polynomial and then integrate.

For Adams-Moulton interpolate $f(t,y)$ at the points $t_{k-1}, t_k, t_{k+1}$ using the Lagrange interpolating polynomial and then integrate.