Define two norms as following: $ \left\Vert f\right\Vert _{1}={ \max_{0\leq x\leq1}\left|f\left(x\right)\right|} , \quad\text{ and }\quad \left\Vert f\right\Vert _{2}={\intop_{0}^{1}\left|f\left(x\right)\right|dx} $
on the vector space $ C\left[0,1\right] $ (the continuous functions).
I need to prove that the two norms aren't equivalent.