Let the domain of the function $f(x) = {\log _2}{\log _4}{\log _6}\left( {3 + 4x - {x^2}} \right)$ be (a, b). If $\int_0^{b - a} {\left[ {{x^2}} \right]} dx = p - \sqrt q - \sqrt r ,p,q,r \in ,\gcd (p,q,r) = 1$, where $[ \cdot ]$ is the greatest integer function, then $p + q + r$ is equal to
