archaic said:
Because the notation ##\int \ldots dx## functions as parenthesis: open and end marks. If you write ##\int dx \ldots ## then it is not clear where the integral ends and other equations start.
However, in physics we often have long expressions as integrands, so it is convenient to a) write the formal signs first and b) make sure from the start what the variable is and what the constants are. As long as one avoids the ambiguity at the end, it doesn't matter. Traditionally is ## dx ## last.
There are a few things where mathematical and physical conventions differ. E.g. whether the Minkowski signature is written ##(+,-,-,-,)## or ##(-,+,+,+)##, or the use of co- and contravariant. Sometimes it is just a way to make the statement: "Hey, I'm a physicist / mathematician!" In the case of integrals, it is because of convenience: If you write ##dx## at the end of a long formula, then you have to read it twice in order to concentrate on the variable and recognize the constants. If you write ##dx## at the beginning, you already know when you inspect the integrand. In cases like ##f(x)=x## then ##\int x\,dx ## looks better than ## \int dx \, x##. But if you have
$$
\int_{-\infty}^\infty \int_{-\infty}^\infty \int_{-\infty}^\infty \dfrac{1}{\sqrt{2\pi}} e^{-i p'x} a^\dagger(p')\dfrac{1}{\sqrt{2\pi}} e^{i px} a(p) \,dpdp'dx
$$
it is somehow easier to read
$$
\int_{-\infty}^\infty dx \int_{-\infty}^\infty dp' \int_{-\infty}^\infty dp \;\dfrac{1}{\sqrt{2\pi}} e^{-i p'x} a^\dagger(p')\dfrac{1}{\sqrt{2\pi}} e^{i px} a(p)
$$
