C++: How can I generate random non-zero intergers in close interval?

I need to create randoms edges in a weighted graph with int non-zero weight. I can't find any solution to create the random generator in c++ able to me return an int with some non-zero value in a range.

my following function can be illustrate better my problem:

/* Non-zero random integer numbers generator in closed interval */
#include <cstdlib>
#include <ctime>

int randomize(int upper_limit, int lower_limit){
    srand(time(NULL));
    int x = 0;
    do
    { 
        x = rand() ...what I need to do?
    }
    while(resp == 0);

    return x;
}