Let f be a (Lebesgue) integrable function and A be a measurable set.

Show that:

$\displaystyle \int lfl\chi_A(x) \leq K*m(A) $ for some K

I know that since f is integrable we can say $\displaystyle \int lfl \leq K $, and this feels like it should be a two line proof, but I can explicitly show how to get to the next step.