Answer
Eq. (11) becomes the standard formula for finding the area under the graph of positive function $f\left(t\right)$.
Work Step by Step
In this case, we have
$x\left( t \right) = t$, $x'\left( t \right) = 1$.
$y\left( t \right) =f\left( t\right)$.
If the $x$-interval is $a \le x \le b$, then the $t$-interval is also $a \le x \le b$.
Eq. (11) becomes
$A = \mathop \smallint \limits_{t = a}^b y\left( t \right)x'\left( t \right){\rm{d}}t = \mathop \smallint \limits_{t = a}^b f\left( t \right){\rm{d}}t$.
This is the standard formula for finding the area under the graph of positive function $f\left(t\right)$.
