Find the area of the region bounded by the graphs of the given equations.
\[
y=2 x^{2}-5 x+6 ; y=x^{2}+5 x-3
\]

Step 1 ：Set the two equations equal to each other to find the points of intersection: \(2x^{2} - 5x + 6 = x^{2} + 5x - 3\).

Step 2 ：Solve the equation to find the solutions, which are the points of intersection. The solutions are \(x = 1\) and \(x = 9\).

Step 3 ：Sort the solutions in ascending order to determine the limits of integration. The lower limit is \(x = 1\) and the upper limit is \(x = 9\).

Step 4 ：Calculate the area between the two curves by integrating the absolute difference of the two functions from the lower limit to the upper limit. The area is \(\frac{256}{3}\).

Step 5 ：Final Answer: The area of the region bounded by the graphs of the given equations is \(\boxed{\frac{256}{3}}\).