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

Because the definite integral depends only on the function and the limits of integration. So writing $\int_{a}^{b} f(x)dt$, $\int_{a}^{b} f(t)dt$, $\int_{a}^{b} f(s)ds$ makes no difference as long as $x$, $t$ and $s$ are "integrated out" in your final answer.  
For more information look here and here (section 7.2).
