When the upper sum $U[f;P]$ equals the lower sum $L[f;P]$ for a measurable partition $P$

Question

I know if there exists a measurable partition $P$ of $[a,b]$, $f$ is Lebesgue integrable on $[a,b]$ when $$ \inf_P U[f;P] = \sup_P L[f;P]$$ where the infemum and supremum are over all measurable partitions.

However, what can I say the function f if $U[f;P]$=$L[f;P]$?