Let ƒ Be an Integrable Function on [A,b], And $s _ { n }$

Multiple Choice

Let ƒ be an integrable function on [a,b], and $s _ { n }$ and $s _ { n }$ be the lower and upper sum of a partition of [a,b], respectively. Which of the following is always true?

A) $s _ { n } = S _ { n }$
B) $\lim _ { n \rightarrow \infty } s _ { n } = \lim _ { n \rightarrow \infty } S _ { n }$
C) $\int _ { a } ^ { b } f ( x ) d x \neq 0$
D) ƒ is continuous on [a,b].
E) $\int _ { a } ^ { b } f ( x ) d x \geq 0$