Recall that the way addition is performed at the bit level discarded the carry out of the leftmost bit position.

For a 32 bit integer, bit positions are numbered 0 to 31 from right (least value bit position) to left (highest value bit position) with bit position k having value 2^k.

Except for 0, to get the negative of a signed integer a we need to find the value b such that

      a + b = 232
   

But the last bit position is 31, not 32. Bit position 32 would correspond to the carry position.

But the carry bit is discarded by the int addition. So the 2³² is discarded leaving 0.

So for signed int type a and b are each the negative of the other if mathematically they add to 2³² - 2's complement.