how can I input an integration equation into this web page?
use the [math][/math] tags.
[math]\int_{a}^{b} f(x) \, dx[/math]
produces
$\displaystyle \int_a^b f(x)\,dx$
(spaces are ignored within the math tag as they are generated logically based on the math, but the \, creates a gentle manual spacing between the function and the dx.)