If … is increasing for … the difference … is the area…

If $v(x)$ is increasing for $a⩽x⩽b$, the difference $S-s$ is the area of the $\underline{}$ rectangle minus the area of the $\underline{}$ rectangle. Those areas approach zero. So every increasing function on $[a,b]$ is Riemann integrable.

If $v(x)$ is increasing for $a\le x\le b,$ the difference $S-s$ is the area of the ____ rectangle minus the area of the ____ rectangle. Those areas approach zero. So every increasing function on $[a,b]$ is Riemann integrable.

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §5.5 The Definite Integral, #25