4 consecutive integers can be represented:
x, x+1, x+2, x+3; their sum is 4x+6=75 which doesn't have an integer solution.
x, x+1, x+2, x+3, x+4 is a sequence of 5 consecutive integers; their sum is 5x+10=75,
x+2=15, so x=13 and the integers are 13, 14, 15, 16, 17.