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

If you're looking at say something like a Riemann integral, you're "adding up pieces". You need some way of keeping track of which piece you're talking about (i.e. of referring to where you are), but it doesn't actually have anything to do with the value of the integral -- it's just a placeholder so you can add up correctly. 
It's essentially the same idea as working with a sum like $a_1+a_2+...+a_n$. If we write it as $\sum_{i=1}^n a_i$, we introduce a variable, $i$ to be able to refer to a particular item ($a_i$ in this case) as we run through the sum. But using $i$ is arbitrary.
The variable could be anything (as long as its not a variable you're already using), it's effectively an accounting convenience - a dummy variable.
