Q: What is a dummy variable?
A: 
and 
are dummy variables because they describe the same pattern.
The indefinite integrals 
and 
are 
dummy variables because they are functionals admitting of different functions.
But if we put an upper and a lower limit to make it a definite integral,
i.e.,
![\begin{aligned} \int_0^1x\,\mathrm{d}x=\bigg[ \frac{x^2}{2} \bigg]_0^1=\frac{1}{2} \\ \int_0^1 y\,\mathrm{d}y=\bigg[ \frac{y^2}{2} \bigg]_0^1=\frac{1}{2} \\ \end{aligned}](https://physicspupil.com/wp-content/ql-cache/quicklatex.com-bd1b02622fcd2262136bf04c0c7269ce_l3.svg "Rendered by QuickLaTeX.com")
,
they are dummy variables as the structure preserves the value.