6, -3, -2
As the sum of the integers is 1, it is clear that at least one of
them is negative. Their product is positive so it may
be deduced that exactly two of the integers are
negative. Now we need to find three factors of 36 such
that the largest is 1 greater than the sum of the other
two. These are 6, 3 and 2.
This problem is taken from the UKMT Mathematical Challenges.