What's a Normalized function?
Similar to a a vector that is normal when it's magnitude is 1, which is the inner product with itself. In the same fashion, a function is normal over a defined range $[t_1,t_2]$ when the root of the integrated squared magnitude is one (if it's normal the root is trivial but this shows the same form as derived from an inner product):
$$||x(t)|| = \sqrt{\int_{t_1}^{t_2}|x(t)|^2dt} = 1 $$
Normalization of functions is done with a simple scaling: If the above formula results in a number of than one, then the entire function is scaled by that number.