Let V = C([-1,1]), with the inner product <f,g> = ∫_{-1,1}f(t)g(t) dt,

and let W be the subspace R_{<=2}[x] ⊂ V, with basis the Legendre polynomials {1, x, 3x^{2}-1}.

Find the projection of the function f(t) = e^{t}onto W using this basis.

I am completely lost there is too much going on in this problem.. and my professor never really explained projections with integrals, or legendre polynomials, etc. Any help?