Upper Darboux Integral: Not Integrable?

[ergonomics]

if a function f is not integrable does it imply, that there exists such an epsilon that whichever partition P i choose it will follow this condition
Uf,p-Lf,p>=Epsilon?

 

[ircdan]

Looks ok yea, f:[a,b]->R not integrable implies there exists an e > 0 such that for all partitions P of [a,b], U - L >= e.

 

[ergonomics]

Thank you.