According to Example 5.9, it has a countably infinite number of discontinuities at rational numbers of $[0\text{,}1]$ (the exception is only $x=0$). To show that $f\in R(a\text{,}b)$ note that ${S}_{\ast}(f\text{,}\mathcal{P})=0$ for every partition $\mathcal{P}$ of $[0\text{,}1]$. Therefore, ${S}_{\ast}(f)=0$ and it remains to ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training,
learning paths, books, interactive tutorials, and more.