Let the first integer be x. Then the next consecutive integer is x + 1. Thus:

x(x + 1) = 272

x^2 + x - 272 = 0

Thus

x = (-1 (+/-) sqrt(1^2 - 4*1*(-272)))/(2*1)

x = (-1 (+/-) sqrt(1 + 1088))/2

x = (-1 (+/-) 33)/2

Thus x = 16 or x = -17

So our two consecutive integers are 16 and 17 or -17 and -16.

-Dan