Calculate the norm of a polynomial knowing inner product

The polynomial $p(x) = 3 - 2x$ is a polynomial in an inner product space with the inner product defined as

$$ \langle p, q \rangle = \int_0^1 p(x)q(x) \, dx$$

on the interval $[0, 1]$ in the vector space $\mathbb{P}^{2}$. The question is to find the norm of $p(x)$, which I know you calculate by doing

$$ \|p(x)\| = \sqrt{\langle p, p \rangle} = \sqrt{\int_0^1 (4x^2-12x+9) dx} $$

I did the problem on my own, and I got the answer $$\|p(x)\| = \sqrt{\frac{13}{3}}.$$

Is this the correct answer? I feel like it would be, but I'm not exactly sure

Yes, your calculations are correct.