For example, say I have an equation that is $\int_0^\infty x g(x)f(x)dx$
Can I calculate each term seperately, say for example my maximum $x$ value is 500.
Is it something like $500\int_0^{500} g(x)\int_0^{500} f(x)dx$?
I could not find a rule for this sort of behavior online, and my background is not in mathematics.
You cannot do this. It's easy to see even in very simple case:
$$ 2 = \int_0^2 1\times 1 \, dx \neq \left(\int_0^2 1\,dx\right)\left(\int_0^2 1\,dx\right) = 2\times 2 $$
Since an integral is essentially a sum, what you propose is something like: $$ a_1b_1 + a_2b_2 = (a_1+a_2)(b_1+b_2). $$ I hope you can see why this doesn't work.