Solution: about the quadratic function of x y=-x? +(2m+2)x-(m？ +4m-3), whose image intersects with the X axis and points A and B (A is on the left of B).

△=(2m+2)？ -4(m？ +4m-3)= 2-m & gt； 0

m & lt2,

Let m be a natural number.

M=0 or m= 1 (discarded).

∴m=0

y=-x？ +2x+3。

A and b are on both sides of the origin,

From Vieta's theorem, we get

x 1+x2=2，

x 1*x2=-3。

| AB | = | X2-x 1 | = √( x2-x 1)

=√(x2+x 1)？ -4x2*x 1？

=√2? -4*(-3)

=√ 16

=4.

By intersecting the y axis at point c.

When x=0 and y=3.

Point C is (0,3).

The height on the base AB of triangle ABC is 3.

∴ area of triangle ABC

=|AB|*3/2

=4*3/2=6.