I need help with this problem.

Let[tex] f(x)[\math] be a bounded function on $\displaystyle [a,b]$. Let $\displaystyle B>0$ and $\displaystyle |f(x)| \leq B$ for $\displaystyle \forall x \in [a,b] $

Show that $\displaystyle U(f^2,P)-L(f^2,P) \leq 2B[U(f,P)-L(f,P)]$ for all partitions P of [a,b]