Prove that <p(x),q(x)>=∫P(x)q(x)ⅆx is an inner product?

Question

I need some help with this problem. Well I already know how to prove first condition (a) and second (b) it's so obvious, but my problem is the third one (c) which states: " $<p(x),p(x)>=0$ if and only if $p(x)=0$ ". Since (c) explicitly states: "If and only If", I don't exactly know how to prove it. I know how to go from $P(x)\geq0$ to an integral but I can't figure out the other way. Can someone please help me ?enter image description here