Originally Posted by

**sponsoredwalk** So the equation of the curve is;

$\displaystyle f(x) = x^2 - 2x - 3$

Well, when finding the area under a curve all you have to do is find the area under the top curve and then subtract the area from the bottom curve;

$\displaystyle

\int_{a}^{b} [f (x) - g(x)]\,dx

$

so, from -1 to 3 we see that the top curve is the x-axis and the bottom curve is f(x), then from 3 to 4 the top curve if f(x) and the bottom curve is y=0

$\displaystyle \int_{-1}^{3} [0 - (x^2 - 2x - 3)]\,dx + \int_{3}^{4} x^2 - 2x - 3 - (0)\,dx $

$\displaystyle \int_{-1}^{3} - x^2 + 2x + 3\,dx + \int_{3}^{4} x^2 - 2x - 3 \,dx $