If f is a function defined on [a,b] which is not continous,then L(P,f)> U(P,f) for any partition P of [a,b].State true or false. Give reason?
false..
Theorem: Let be a bounded function. Then and exist; and ..
the theorem does not have any condition on to be continuous or not, thus it holds for any bounded function
if you have not seen that theorem, you may use a counter-example (Modified Dirichlet Function).
if
if
and show that L(P,f) < U(P,f)