Could some one tell me how to get started on this problem?

Find the space orthogonal to the space spanned by $\displaystyle \left \{ x^{3}, x+1 \right \}$ with respect to the inner product as defined by: $\displaystyle <f, g> = \int_{1}^{4} fg\mathrm{d}x$

I understand how to deal with inner products, but I don't know how to find what the space orthogonal to the space spanned is. Any information will be appreciated.