Javascript Random Integer Between two Numbers

I'm trying to create a random number generator that generates random numbers between two numbers. For instance, let's say I want to generate a random number between 4 and 10, I would want it to be able to choose from any number from 4 - 10. Here is what I tried:

var randNumMin = 4;
var randNumMax = 10;
var randInt = (Math.floor(Math.random() * (randNumMax - randNumMin + 1)) + randNumMin);

However, that didn't seem to work and generated weird random numbers that weren't between 4 and 10, and some began with 0. What would be the correct algorithm to do this?

Here is the code I'm implementing the algorithm in:

$(function() {
    $('#generateRandNums').click(function() {

        var numCount = document.getElementById("randNumCount").value;
        var randNumMin = document.getElementById("randNumMin").value;
        var randNumMax = document.getElementById("randNumMax").value;

        if (numCount.match(/^[\d]*$/ ) && randNumMin.match(/^[\d]*$/ ) && randNumMax.match(/^[\d]*$/ )) {       
            if (numCount == "" || randNumMin == "" || randNumMax == "")  {
                alert ("Please fill out all forms then try again.");

            } else {
                if (randNumMin>randNumMax) {
                    alert ("Please make sure your first number is smaller than the second, then try again.");
                } else {
                    if (randNumMin<0) {
                        alert ("Please make sure that you generate a positive number of random numbers, then try again.");
                    } else {

                        if (numCount>1) {
                            var randResult = ("You generated " + numCount + " random numbers between " + randNumMin + " and " + randNumMax + " and got the numbers ")
                            oneNumber = 0;
                        } else {
                            var randResult = ("You generated a random number between " +