Chasle relation with arbitrary ordering of endpoints. Consider the Chasle relation :
$$\int_a^c f(x) dx= \int_a^b f(x) dx+ \int_b^c f(x) dx\,$$
Is this only true for $a\leq b\leq c$ or is it true for any ordering of $a,b$ and $c$ ?
In the case  $a\leq b\leq c$, we have the interpretation that the area under the curve delimited by $a$ and $c$, is the sum of the areas under the curves delimited by $a$ and $b$ and under $b$ and $c$, but with an arbitrary ordering I could not see an interpretation. Thank you for your help!

Assume $a \leq c \leq b$
Now
$$\int_a^c f(x) dx =\int_a^b f(x) dx + \int_b^c f(x) dx  $$
Since $c \leq b$ we can do
$$\int_a^c f(x) dx =\int_a^b f(x) dx - \int_c^b f(x) dx  $$
You see that if the ordering changes the signs change, too. 
