Examples Let be the function which takes the value 1 at every point. Any Riemann sum of on will have the value 1, therefore the Riemann integral of on is 1.
ExAmPLes lEt be The funcTion Which takes tHE VaLue 1 aT eVeRy point anY RIemann Sum OF on will HAVe the VAlue 1 therefOre thE rIeMANN InteGRAl oF on iS 1