An integral is a limit of signed rectangle areas. More, thinner rectangles usually improve the approximation.
Each rectangle contributes height times signed width. For the continuous functions here, the sums converge as the mesh tends to zero. Reversing the bounds reverses the signed integral. Geometric area instead integrates |f| from the smaller bound to the larger.
Regions below the axis contribute negatively to a signed integral.
Negative heights and reversed bounds retain their signs. Geometric area is a numerical estimate of ∫|f| over the ordered bounds.