Category:Sum of Integrals on Adjacent Intervals for Integrable Functions

This category contains pages concerning Sum of Integrals on Adjacent Intervals for Integrable Functions:

Let $f$ be a real function which is Darboux integrable on any closed interval $\mathbb I$.

Let $a, b, c \in \mathbb I$.

Then:

$\ds \int_a^c \map f t \rd t + \int_c^b \map f t \rd t = \int_a^b \map f t \rd t$