Use the Fundamental Theorem of Calculus to find the "area under curve" of $y=-x^{2}+7 x$ between $x=2$ and $x=6$. In your calculations, if you need to round, do not do so until the very end of the problem.
Answer:

Step 1 ：First, we need to find the integral of the function \(y=-x^{2}+7 x\) from 2 to 6. This is done using the Fundamental Theorem of Calculus, which states that if a function is continuous over the interval [a, b], then the integral of the function from a to b is equal to the antiderivative of the function evaluated at b minus the antiderivative of the function evaluated at a.

Step 2 ：The antiderivative of \(-x^{2}+7 x\) is \(-\frac{1}{3}x^{3}+\frac{7}{2}x^{2}\).

Step 3 ：We evaluate this antiderivative at 6 and 2 and subtract the two results.

Step 4 ：The final calculation gives us the area under the curve of \(y=-x^{2}+7 x\) between \(x=2\) and \(x=6\).

Step 5 ：Final Answer: The area under the curve of \(y=-x^{2}+7 x\) between \(x=2\) and \(x=6\) is \(\boxed{\frac{128}{3}}\).