I need to express the area of the region as a definite integral.
f(x)=-x^(2)-2x+3
Thanks for your help.
$\displaystyle \int_{a}^{b}{f(x)}dx = F(b) - F(a)$
where F is the antiderivative of f(x)
You need to give us the a and b so that we can tell you the area of the reagion.
For example if you want the area of a region of f(x)=-x^(2)-2x+3 from x=0 to x=6
the answer should be
$\displaystyle \int_{0}^{6}{(-x^{2}-2x+3)} dx$