The value of the integral $\begin{align*} \int_4^{10} \frac{[x^2]dx}{[x^2 -28x + 196] + [x^2] } , \end{align*}$ where $[x]$ denotes the greatest integer less than or equal to $x,$ is :

Question

$\begin{array}{1 1}(1)\; 6 \\(2)\; 3 \\(3)\; 7 \\ (4)\; \frac{1}{3} \end{array} $