I am working through part of my book which deals with area of curvilinear trapezoid.
I am getting this inequality $s\leq P_1 \leq P_2 \leq S$ where $s=\sum_{n=1}^n m_i \Delta x_i$
$S=\sum_{n=1}^n M_i \Delta x_i$ which are respectively darboux lower and upper integral sums.For answering question you don't need to know what is $P_1,P_2$ here.
Then book says because $f$ is integrable then $I=\int_a^bf(x)dx$ is only number that regardless of split will satisfy $s \leq I \leq S$.
I know that $s \leq I \leq S$ but I can't understand from where we got that it is only number between those?