The problem is: Prove that iffis continuous at x0, an element of [a,b], and f(x0)=/ 0, then the lower intergral from a to b of the absolute value of f(x) is >0.

I am supposed to use the Sign Preserving Property, but I don't see how to set this up to make it work. I can see that I have to prove that either the abs. value of the inf{L(f,P): P is a partition of [a,b]} or the abs. value of the sup {L(f,P): P is a partition of [a,b]} >0 but I don't see the beginning steps of it.