#include <iostream>
using namespace std;
int main() {
    int n, res = 0;
    cin >> n;
    if (n < 0) {
        for (int i = -2; i >= n; i--) {
            res = res + i;
            }
        cout << res;
    }
    else {
        for (int i = 1; i <= n; i++) {
            res = res + i;
        }
        cout << res;
    }
    return 0;
}

int i = -2; i >= n; i--    i = 1

Optimization trick with initial i=-2 is funny.
But now you aren't processing case "n == 0" correctly.

if(n == 0) --> ans = ? bro.. i don't understand... i'm from vietnam

Lets read task:
> sum of all integer numbers lying between 1 and N inclusive

If N==0 then set of integers to sum is [0..1], sum is 1.