What is the dx for in high school integrals?

(1) Tradition.
(2) It helps you remember what variable you are integrating with respect to
  (you could do \int_{x=0}^17 f instead though...)
(3) change of variables (er, u substitution)
 (e.g., if you want to find \int 2x, you could naively say u=2x, so
 \int 2x = \int u = \frac{1}{2}u^2 = 2x^2, which is wrong)

(I think 3 is the primary reason)

Valid reasons that it's there:
(4) You need to integrate with respect to a measure, so dx is Lebesgue measure
(5) You're integrating a $1$-form.

(I think 5 is the only valid reason - we could denote measure by \mu instead
 of d\mu)

note: an $n$-form is something that restricts to a measure on an $n$-dim'l
submanifold.