How to count the number of integers in a file in C?

while(!feof(file)){
    fscanf(file, "%d", &array[count]);
    count++;
}

Instead of checking for eof, you need to check the returncode of fscanf():

while(fscanf(file, "%d", &array[count]) == 1)
    count++;

But it would be better to build in some safety too, like:

#define NUM_ITEMS 1000
int array[NUM_ITEMS];
int main(int argc, char* argv[]){
{
    FILE* file;
    int i, count = 0;
    file = fopen(argv[1], "r");
    if (!file) {
        printf("Problem with opening file\n");
        return 0; // or some error code
    }
    while(count < NUM_ITEMS && fscanf(file, "%d", &array[count]) == 1)
        count++;
    fclose(file);
    for(i=0; i        printf("a[%d] = %d\n", i, array[i]);
    }
    return 0;
}