Why Do We Write Dx?

In the context of integration, remember that an integral is a limit of a Reimann sum (areas of rectangles). Δx in this case corresponds to the width of a rectangle. When you take the limit, Δx goes to 0, and by some consequence of definition, it gets denoted by dx which is the same idea as above. I really don't know why this is.

d is used to denote an infinititesimally small delta. Integrals can only be taken on differentials, you cannot integrate a delta x, or an x. That doesn't make sense.