I need to give an example of a function $f:[a,b]\rightarrow\mathbb{R}$ that is in $R[c,b]$ for every $c\in (a,b)$ but which is not in $R[a,b]$
I need to give an example of a function $f:[a,b]\rightarrow\mathbb{R}$ that is in $R[c,b]$ for every $c\in (a,b)$ but which is not in $R[a,b]$
How about $f(x)=\begin{cases} \frac{1}{x} & \mbox{if}\quad x>0 \\ 0 & \mbox{if} \quad x=0\end{cases}$?