I made the following assertion on an exam I thought was true:
If a function is Riemann-integrable on $[a,b]$ then it attains its maximum on the interval.
Apparently this is false. This is definitely true if $f$ is continuous. Thus I'm trying to argue that there exists a discontinuous function that is Riemann-integrable and does not attain its max on the interval. I'm having a tough time though -- ideas?
Edit: Sorry for all the edits!