If f and g are both Riemann integrable on [a,b], prove that fg is also Riemann integrable.

This is what I've got so far...

Let ||f||∞= sup{|f(x)|: x E [a,b]}

= sup{f(x): ≤ x ≤ }

= inf{f(x): ≤ x ≤ } where P is a partition of [a,b]

Let x,t E [ ]

Then |f(x)g(x)-f(t)g(t)| ≤ |f(x)| |g(x)-g(t)| + |f(x)-f(t)| |g(t)| ≤ ||f||∞ [ ] + [ ] ||g||∞

Any help is appreciated!

[also under discussion in math links forum]