Mathematics Question from JEE Main 2025 · 3 April, Shift 1

Let the domain of the function $f(x) = \log_2 \log_4 \log_6 (3 + 4x - x^2)$ be $(a, b)$. If $\int_0^{b-a} [x^2] \, dx = p - \sqrt{q} - \sqrt{r}$, $p, q, r \in \mathbb{N}$, $\gcd(p, q, r) = 1$, where $[.]$ is the greatest integer function, then $p + q + r$ is equal to