What is the signed area between the curve y = x^2 - 4 and the x-axis?

The curve y = x^2 - 4 is a parabola that crosses the x axis at x = - 2 and x = 2, so the area that we are looking for is the area within the parabola when y <= 0 and -2<= x <= 2. So we expect our area to be negative, as this part of the graph of the curve lies under the x-axis.To find the area we integrate the function x^2 - 4 between -2 and 2.The solution to the integral is [x^3/3 -4x] evaluated at 2 minus [x^3/3 -4x] evaluated at -2. That will give the result 16/3 - 16 = -32/3. So the signed area is -32/3 and this is negative as expected.