show that ||f||1 = ∫|f| (integral from 0 to 1) does define a norm on the subspace C[0,1] of continuous functions

(there are 3 conditions , i just dont know how to prove that ||v||>0,||v||=0 implies v=0)

and also the same for ||f||= ∫t|f(t)|dt is a norm on C[0,1]