Find the value of A to normalize the wave function: {A, -L

Hello!
There is no given L and no given A. But, this is not a problem, we can write expressions with variables.
To normalize a wave function means to find the expression for A (depending on L) such that the probability of finding a particle somewhere on the entire axis is exactly 1. It is known that a probability density function pd(x) is the square of a wave function Psi(x).
Also, by the definition of a probability density function, the probability of a particle being (at least) somewhere is  int_(-oo)^(+oo) pd(x) dx = int_(-oo)^(+oo) |Psi(x)|^2 dx. 
 
In our case Psi(x) = 0 for x outside [-L,L], therefore the integral is equal to
int_(-L)^(+L) |Psi(x)|^2 dx = int_(-L)^(+L) |A|^2 dx = 2LA^2,
and this must be 1, so A^2 = 1/(2L),  A = 1/sqrt(2L). This is the answer.