lower integral meaning in Hindi

Examples

1. Finally L consists of those functions whose upper and lower integrals are finite and coincide, and
2. Chordioids is related also to upper structures as a technique insofar as upper structures represent groups of notes not commonly taken to be " legitimate " chords, but differs in that chordioids as a technique uses " a priori " structures held in common rather than a free selection of color tones appropriate for a lower integral chord.
3. I have that a function is Riemann integrable if its upper and lower integrals are equal, or alternatively if for any \ epsilon there exists some dissection D with U ( f, D )-L ( f, D ), but I don't really know how to start proving that in this example case . ..