Shifted Legendre Polynomial

Hi:

I'm kinda confused about Legendre Polynomial.

SO if i was to calculate the orthogonal polynomials int eh interval [0,1]

can't i do soemthing like this:

p0 = 1

p1 = x - c0 p0

such that Integral p0p1 over the interval [0, 1] shd be zero. After solving for p1 I get

c0 = 1/2

p1 = x - 1/2

but the actual shifted legendre polynomial for p1 = (1-2t)

I don't understand as to how to calculate orthonormal/orthogonal polynomials in a particular interval. I'd really appreciate if someone could explain me the subtleties of the gram-schmidt.