When you add 1 to INT_MAX, the value wraps around to INT_MIN. This is called overflow. Your program does not crash - it just gives you the wrong answer. Example: if int x = 2147483647; and you do x = x + 1;, you get -2,147,483,648 instead of 2,147,483,648.
The calculation silently breaks. Overflow happens when you multiply two large numbers or sum many values. Always check if your numbers might exceed 2 billion.