Are you allowed to substitute for imaginary numbers on a real integral?

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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?