I am trying to design a question that makes sense.
First, I consider the greatest integer function on an interval$ [1,5]$. This throws up $1,2,3,4$ and $5$. Then I wish to permute these numbers by $(1 3 2)(4 5)$. This means all the $x$ which lies on $[1,2)$ gets mapped to $3$, all the $x$ which lies on $[2,3)$ gets mapped to $1$ and so forth.
Next, I want to ask people to test its Riemann Integrability over $[1,5]$. Of course, it is not!
Well, would it make sense if I ask-
Let $f:[1,5] \to R , h:[1,5] \to R$ and $ g=(1 3 2)(4 5)$ where
$f$ is the function composition given by $f= goh$, $h(x) = [x]$ is the greatest integer function of $x \in [1,5]$ and $g = (1 3 2)(4 5)$.
If $f$ a Riemann Integrable function on $[1,5]$?