Define on $P3$ the inner product $<f,g>=\int_{-1}^1 f(t)g(t)dt$, find orthogonal projection

Question

Define on $P3$ the inner product $\langle f,g \rangle=\int_{-1}^1 f(t)g(t)dt$.

a) find the orthogonal projection of $p(x)=x^3$ onto $P2$

I know the orthogonal projection formula, but how do I solve it without knowing $f(t)$ and $g(t)$?

I also have a hard time in turns of proving the Positive Definite Property of this inner product.