Bounded interval/Real Function/Step integral from above/Definition

Step integral from above

Let $I$ denote a bounded interval, and let

$f:I⟶ℝ$

denote a function. For a step function from above

$t:I⟶ℝ$

of $f$, with respect to the partition $a_i$, $i=0,\dots ,n$, and values $t_i$, $i=1,\dots ,n$, the step integral

$T:=\sum _{i=1}^n{t}_i(a_i-a_{i-1})$

is called a step integral from above for $f$ on $I$.