Why do we use dummy variables in integrals? I want to know why we use dummy variables in integrals?

I'll interpret the question as

Why are we not using the orignal one instead of a dummy variable?
  Why use $\int_0^xf(x')dx'$ and not $\int_0^xf(x)dx$?  

(If this is the case, please clarify you question with an marked(!) edit, others interpreted in differently.)
Because it has a different meaning and there is a problem with how to define it.
To show the difference define
$$g(x):= \int_0^xf(x,x')dx'$$
for some $f:\mathbb{R}^2\to \mathbb{R},(x,y)\mapsto f(x,y)$ continuously differentiable with respect to both arguments (being only continuous instead of differentiable would be enough).
Now compute
$$\frac{dg(x)}{dx}= \frac{d}{dx}\int_0^xf(x,x')dx' =f(x,x) +\int_0^x\frac{df(x,x')}{dx}dx' =f(x,x) + \int_0^x f_1(x,x')dx',$$
where $f_1$ means the first partial derivative of $f$.
The right part happens, because the inner part of the integral was dependend of the outher variable $x$.
So $\int_0^xf(x,x')dx'$ means something different from $\int_0^xf(x',x')dx'$
This is the reason why 
$$\int_0^xf(x,x)dx$$ 
is somewhat not well defined.
