To find the area between the curves, we first need to determine their points of intersection.
y = x^2 + 6 and y = (x-3)^2 + 4x - 7
Equate the two
x^2 + 6 = (x - 3)^2 + 4x - 7
=> x^2 + 6 = x^2 + 9 - 6x + 4x - 7
=> 4 = -2x
=> x = -2
y = 10
We see that the two curves intersect at only one point. Therefore we cannot find the area of the region enclosed between them.