So, lets assume I am give this integral:
$$\int_{a}^b f(x)\text{d}x$$
where $a,b,c\in\Bbb{R}$ and $f:\Bbb{R}\to\Bbb{R}$
Are you allowed to make the following substitution?
Substitute $x=ci$
That (in my mind) will make the integral come out to $$\int_{ia}^{ib} if(c)\text{d}c$$
I don't know if something like that is allowed? Is it?