The integral test states that given a function $f(n)$ that is positive, continuous, and decreasing on the interval $x \geq 1$, and a series $a_n = f(n)$, $\int_1^\infty f(n)dn$ and $\sum_{n=1}^\infty{a_n}$ either both converge or diverge.
Is this not necessarily true for negative, continuous, increasing functions? Why so?
If $f$ is negative, increasing and continuous, you can apply the integral test to $b_n=-a_n=-f(n)$...