non existence of weak derivative evans pde chapter 5 example 2

Question

Hi Im looking at the this very basic example, in proving the non existence of weak derivative.

I am confused in the last line $$\cdots\lim_{m\to\infty}\left(\int_0^2 v\phi_m dx-\int_0^1\phi_m dx\right)=0$$.

Could anyone show me how this could be 0? I tried but my answer was 1...

Thanks!