It becomes clear that some of the integers must be negative. You can factor $45$ first to get $45=3^{2} \cdot 5 \cdot 1$. Clearly, you must have an even amount, so you get the factorization: $45=1 \cdot -1 \cdot 3 \cdot -3 \cdot 5$, so the sum becomes just $\boxed{5}$