calculus - $dyover dx$ is one things but why in integration we can treat it as 2 different terms

when i am learning differentiation, my lectuer tell us that the deriative $dy\over dx$ is one things, it is not the ration between dy and dx. However when i learn
about integrating, sometime we need to do substitution, like integrating $\int_{0}^{1}2xdx$ when substituting $y=2x$, we can substitute $dy=2dx$, but why in this case it can be treated as 2 different terms instead of 1 term??