quantum mechanics - Normalizing a set of eigenfunctions with different domains

Maybe it seems so easy, but it is not!

How can we obtain the normalization constant $N$ for a set of eigenfunctions with different domains?

For example, we have

$\psi_{1}=N(f_{1}e^{-\kappa x}+g_{1}e^{\kappa x}),\hspace{1cm}x\in[0,1],\hspace{.2cm} \nonumber \\ \psi_{2}=N(f_{2}e^{-\kappa x}+g_{2}e^{\kappa x}),\hspace{1cm}x\in[0,1], \hspace{.2cm} \nonumber \\ \psi_{3}=N(f_{3}e^{-\kappa x}+g_{3}e^{\kappa x}),\hspace{1cm}x\in[-1,0], \\ \psi_{4}=N(f_{4}e^{-\kappa x}+g_{4}e^{\kappa x}),\hspace{1cm}x\in[-1,0].\nonumber$.

we can normalize each wavefunction by the integral $\int^{x2}_{x1}\psi^{*}\psi dx=1$, but that way, the other eigenfunctions are not normalized to one!