- Let $\displaystyle f:[a,b]\to\mathbb R$ be a monotone function on the compact interval $\displaystyle [a,b].$ Prove that $\displaystyle f$ is integrable on $\displaystyle [a,b].$
- Let $\displaystyle f:[a,b]\to\mathbb R$ be a continuous function on the compact interval $\displaystyle [a,b].$ Prove that $\displaystyle f$ is integrable on $\displaystyle [a,b].$

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