Sum Of Numbers Between Two Integers

I was trying to get sum of numbers between two given integer and managed to do it.

public int sum(int a, int b) {
int sum=0;
while(a <= b) {
sum+=a;
a++;
}
return sum;
}

in here; when I enter the values i.e 2 and 5, it calculates 2+3+4+5 and gives me the result 14.

my question is, how could I exclude a and b in this calculation ( in this case exclude 2 and 5 and return 3+4 )

Bonus question ; how could I only calculate the odd (or even) numbers between those integers?