2019 AMC 12A Problem 4

Negative integers are allowed. The integers from $-44$ to $44$ sum to $0,$ so the integers from $-44$ to $45$ sum to $45.$ This run has $45 - (-44) + 1 = 90$ integers. Conversely, if $L$ consecutive integers have sum $45,$ then twice their sum is $L$ times an integer, so $90$ is a multiple of $L.$ Hence $L\le90,$ proving that this run is longest. Thus, the correct answer is D.