Wavelet zero mean condition

Question

I'm trying to understand more about wavelets so I went and read the wikipedia article and some other papers on the topic. I have learned that wavelet functions are compact supported and belong to the space $L^1(\mathbb{R})\cap L^2(\mathbb{R})$ i.e. $$\int^\infty_{-\infty}|\psi(t)|\,dt<\infty\quad\rm{and}\quad\int^\infty_{-\infty}|\psi(t)|^2\,dt<\infty.\qquad\qquad(1)$$ However I don't see why the previous conditions imply that $$\int^\infty_{-\infty}\psi(t)\,dt=0\quad\rm{zero\,mean\,condition}\qquad\qquad (2)$$ and $$ \int^\infty_{-\infty}|\psi(t)|^2\,dt=1.\qquad\qquad(3)$$ The previous equations appear in https://en.wikipedia.org/wiki/Wavelet#Mother_wavelet so I would like to know why (1) implies (2) and (3). Thank you for your help.