Hey cummings123321.

For the ||v|| > 0 consider the definition of the integral and how you partition it up and add up these partitions. Each partition will be positive which means the norm will be positive and zero only if all elements are zero since the sum of all positive things can only be zero if all are zero.

You will need to specify what kind of integral you are using (because it won't be the Riemann integral for C[0,1]).