# Submartingale help

How do i show that $(B_t^2 -t)^2$ is a submartingale w.r.t. the natural filtration generated by $B_t$ , where $B_t$ is a standard Brownian motion started at zero....
Apply Ito's formula to $f(t,B) = (B_t^2-t)^2$.
$4\int_0^t B^2(u)du$
$E[4\int_0^t B^2(u)du | F(s)] \geq 4\int_0^s B^2(u)du, 0 \leq s \leq t$ and thus f(t,B) is a submartingale.