Find the area between the curves.
\[
x=-5, x=1, y=6 x, y=x^{2}-7
\]

Set up the integral (or integrals) needed to compute this area. Use the smallest possible number of integrals. Select the correct choice below and fill in the answer boxes to complete your choice.
A. $\int_{-5}[] d x$
B. $\int_{-5}^{-1}[\square] d x+\int_{-1}^{1}[\square] d x$

The area between the curves is $\square$.
(Simplify your answer.)

Step 1 ：Set the two equations equal to each other to find the points of intersection: \(6x = x^2 - 7\)

Step 2 ：Rearrange the equation to form a quadratic equation: \(x^2 - 6x - 7 = 0\)

Step 3 ：Factor the quadratic equation to find the roots: \((x - 7)(x + 1) = 0\)

Step 4 ：The points of intersection are \(x = -1\) and \(x = 7\)

Step 5 ：We are only interested in the region between \(x = -5\) and \(x = 1\)

Step 6 ：For \(x\) between \(-5\) and \(-1\), the curve \(y = 6x\) is above the curve \(y = x^2 - 7\)

Step 7 ：For \(x\) between \(-1\) and \(1\), the curve \(y = x^2 - 7\) is above the curve \(y = 6x\)

Step 8 ：The area between the curves is given by the integral \(\int_{-5}^{-1}[(6x) - (x^2 - 7)] dx + \int_{-1}^{1}[(x^2 - 7) - (6x)] dx\)

Step 9 ：Simplify the integrals to get \(\int_{-5}^{-1}[-x^2 + 6x + 7] dx + \int_{-1}^{1}[x^2 - 6x + 7] dx\)

Step 10 ：\(\boxed{\int_{-5}^{-1}[-x^2 + 6x + 7] dx + \int_{-1}^{1}[x^2 - 6x + 7] dx}\) is the final answer