the integer are called, a, b, c
if they are consecutive that means that:
b = a + 1
c = a + 2
and we know that they add to -34, that is:
a + b + c = -34
lets substitute the first two equations in the third:
a + b + c = -34
a + (a + 1) + (a + 2) = -34
3a + 3 = - 34
3a = -37
a = -37/3
the first number is -37/3, therefore there aren't integers consecutive that sum -34
