Answer
See graph
Intersection points area
$(0, -6)$ and $(3, 6)$
Work Step by Step
$f(x) = -x^2 + 7x - 6$
$g(x) = x^2 + x - 6$
Solving $f(x) = g(x)$
$ => -x^2 + 7x - 6 = x^2 + x - 6$
$=> 2x^2 - 6x = 0$
$=> x^2 - 3x = 0$
$=> x(x-3) = 0$
$=> x = 0, 3$
$f(0) = g(0) = -6$
$f(3) = g(3) = 6$
Intersection points area
$(0, -6)$ and $(3, 6)$