Proper Wavefunctions ( ψ ) in Quantum Mechanics Must Be $\int_{-\infty}^{\infty}[\psi(x)]^{2} d x=1$

Multiple Choice

Proper wavefunctions ( ψ ) in quantum mechanics must be normalized. Which statement below best summarizes this mathematically?

A) $\int_{-\infty}^{\infty}[\psi(x) ]^{2} d x=1$
B) $\int_{-\infty}^{\infty} \psi(x) d x=1$
C) $\int_{-\infty}^{\infty}[\psi(x) ]^{2} d x=0$
D) $\lim _{x \rightarrow \infty}$ $\psi(x) =0$
E) $\psi(x) =\sin \left(\frac{n \pi x}{L}\right) ; n=1,2,3 \ldots$