Finding a basis for the subspace of P_2

**Problem Statement:**

Let $\displaystyle p(x), q(x) \in P_2$. You may assume that

<$\displaystyle p(x), q(x)$> $\displaystyle = \int_{-1}^1 p(x)q(x)dx$

defines an inner product on $\displaystyle P_2$

Find a basis for the subspace of $\displaystyle P_2$:

$\displaystyle V = \{ a + b + ax + bx^2 | a,b \in R\}$

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I'm sure this is a very easy question, just not sure how to go about it. Would we not just use as the basis the standard basis of $\displaystyle P_2$, i.e.,

$\displaystyle \{1, x, x^2\}$?

Note: I'm not sure if the inner product is important for answering this specific question, as there is another question that follows to which it may apply instead.