Evaluation of a Bounded Plane Area by Integration

Section 9.2.1's Remarks already connected the sign of $\int_a^b f(x)\,dx$ to geometric area — a non-negative integrand yields area directly. This section turns that observation into ready-to-use area formulas for the region bounded by a curve and the coordinate axes (§9.8.1 for the $x$-axis, §9.8.2 for the $y$-axis) and between two curves (§9.8.3), each derived from the same limi …