Evaluate. \[ \int_{2}^{3}\left(5 x^{2}+6\right) d x \] $\int_{2}^{3}\left(5 x^{2}+6\right) d x=\square$ (Type an integer or a simplified fraction.)

Step 1 ：The function to be integrated is \(5x^2 + 6\).

Step 2 ：The antiderivative of \(5x^2\) is \(\frac{5}{3}x^3\) and the antiderivative of \(6\) is \(6x\).

Step 3 ：So, the antiderivative of the function is \(\frac{5}{3}x^3 + 6x\).

Step 4 ：We need to evaluate this antiderivative at \(x = 3\) and \(x = 2\) and subtract the two results to find the definite integral.

Step 5 ：The definite integral of the function \(5x^2 + 6\) from \(2\) to \(3\) is \(\boxed{\frac{113}{3}}\).