Say there are two integers that are both negative, and you subtract them. would the answer be positive, or remain negative?

It depends upon the numbers...If both are negative numbers, then you change the value of the second number and add them. For example:
(-3) - (-6) = (-3) + 6 = 3.

(-7) - (-4) = (-7) + 4  = -3

So, it depends on the second numbers sign.

I hope this answer helped you :)