How can I represent integer intervals in Java?

Check apache commons-lang IntRange. So, if you want to check if a number is in a given interval (range), you do:

IntRange range = new IntRange(-4, 3);
if (range.contains(x)) {
   ....
}

You simply have to separate -4 < x < 3 into -4 < x and x < 3, like this:

if (-4 < x && x < 3)
{
. . .
}

Google Guava also has a Range class (https://guava.dev/releases/19.0/api/docs/com/google/common/collect/Range.html) that may work for you.