Probability of electron in a box problem

Homework Statement

Calculate the probability that an electron will be found (a) between x = 0.1 and 0.2 nm, (b) between 4.9 and 5.2 nm in a box of length L = 10 nm when its wavefunction is psi = (2/L)^1/2 sin(2*pi*x/L).

Homework Equations

As far as I know, only the normalization equation, which is A^2 * Integral(psi^2) = 1

The Attempt at a Solution

My problem is actually how to start it. Should I assume that the wavefunction is already normalized, or should I normalize the wavefunction by equating the integral of the squared wavefunction to 1, then solve for A? Sorry if wording of the question is bad. Any help is appreciated.

It looks like the wavefunction is already normalized. Its easy to check.

The fundamental principle of the probabilistic interpretation of quantum mechanics is that the probability of finding a particle between points a and b, is equal to the integral of the wave-function squared over that interval:

$$P(a<x<b) = \int_a^b |\Psi(x) |^2 dx$$

I was able to solve it, thanks!

Given two normalized but non-orthogonal eigen functions, psi=(1/sqrt(pi))exp(-r) and phi=(1/sqrt(3pi))rexp(-r). Construct a new function PSI which is orthogonal to the first function and is normalized.

Can any one help me please?

Many many thanks for your kind help.

MSPNS