Use the inner product $$\langle f,g\rangle = \int_0^1 f(x)g(x) \, dx$$ in the vector space $C^0\lbrack 0,1\rbrack$ of continuous functions on the domain $\lbrack 0, 1 \rbrack$ to find the orthogonal projection of $f(x) = 3 x^2 + 1$ onto the subspace $V$ spanned by $g(x) = x$ and $h(x) = 1$. (Caution: $x$ and $1$ do not form an orthogonal basis of $V$.)

${\rm proj}_V(f) =$ .