Which integrable functions have the property that all lower sums are equal?
This is from Spivak's Calculus (a * problem). The question mentions the use of dense sets as a hint as well as the fact that if f is integrable on [a,b] then f must be continuous at many points in [a,b]
My question is, doesn't a constant function satisfy this? The lower sums (as well as the upper sums) will be all equal regardless of the partition... I guess I'm underthinking this. Can anybody help see where my thinking goes wrong and how I should proceed?