1. ( 8 points) Find the area enclosed by the curves $y=x^{2}-5 x-7$ and $y=x-12$ over the interval $[-2,5]$. Draw the graphs and shade the desired area.

Step 1 ：First, we need to find the points of intersection of the two curves $y=x^{2}-5 x-7$ and $y=x-12$ over the interval $[-2,5]$. This is done by setting the two equations equal to each other and solving for $x$.

Step 2 ：The solutions to the equation are $x=1$ and $x=5$.

Step 3 ：Next, we calculate the area enclosed by the two curves. This is done by integrating the absolute difference of the two functions over the given interval. In this case, we need to find the integral of |(x^2 - 5x - 7) - (x - 12)| from -2 to 5.

Step 4 ：However, to do this, we need to know where the two functions intersect within this interval, as this will determine which function is the upper function and which is the lower function.

Step 5 ：By calculating the integral, we find that the area enclosed by the curves is approximately 10.67 square units.