One of the problems is that you never initialize your variable
total before you start using it. So you are bound to get unpredictable results in your output. It is always a good idea to initialize your variables.
You might also want to display the value of total after the loop has completed iterating.
CODE
int main()
{
int num1, num2, total = 0;
cout << "This program will display a range of numbers according to what you have\ninputted\n";
cout << "\nEnter your first number: ";
cin >> num1;
cout << "\nEnter your second number: ";
cin >> num2;
cout << "\nYour range of numbers are: \n";
for (int num = num1 + 1; num <= num2 - 1; num++)
{
total = total + num;
cout << "\t" << setw(3) << num;
}
cout << "\n" << setw(3) << total;
cout << "\n\n";
system("pause");
return 0;
}