• returning negative number instead of zero is WRONG
• int can overflow to positive value as well

mwrum, your solution is not correct either.
The expression (sum + i > Integer.MAX_VALUE) is always false if sum and i are both integers (at least one should be long), because the sum will overflow and become negative.

I disagree. If int overflows, it wraps and goes to negative. Returning a negative number is clearly not mathematically correct, therefore zero should be returned.

Counter question: What happens if there is an integer overflow in Java? - Right, it goes back to min value which is < 0.

Thus, no requirements have been ignored.

Why are all the accepted and upvoted solutions ignoring the requirement that out of range values (ie. any sum greater than Integer.MAX_VALUE) should be zero?