Convergence of improper integrals $\int_{-\infty}^{\infty}f(x)dx$ and $\int_{-\infty}^{\infty}f^{2}(x)dx$

Question

(1) Convergence of $\int_{-\infty}^{\infty}f(x)dx$. (2) Convergence of $\int_{-\infty}^{\infty}f^{2}(x)dx$

What is the relationship betweeen the two? (i,e is there any logical relations...?) (1 implies 2 or 2 implies 1)