Solution:

Note that negative integers are allowed to be in the sequence.

This means that we could form the sequence $$-44, -43, \cdots, 44, 45,$$ which clearly adds up to $45.$ There are $90$ terms in this sequence.

Adding another negative term wouldn't work, since that would require having to go up to $46$ in the positive numbers, which puts the sum over $45.$

Thus, D is the correct answer.