SOLUTION: compute the area between y=|x| and y=x^2-6

First make sure that all possible vertical line segments drawn from
the upper boundary of area to lower boundary are such that they all
begin on one curve and end on the other.  If so, then

Area between two curves = 

We draw the graph of the two curves:



y=|x| is really this piece-wise function:

 

We find the point of intersection:






x-3=-0   x+2=0
  x=3      
y=x       (not pertinent)
y=3

The point of intersection is (3,3)

By symmetry we can find the area of the right half
from x=0 to x=3 and then double it.




 
Edwin