I'm trying to understand the proof of this function:

Here is the part that I understand:

Let

Then,

But then, they go on to state this, which I can't figure out:

What I don't understand is how the x-squared terms can always be either less than -1 or greater than 1. I understand that the middle term oscillates between -1 and 1, but how do we know what x-squared is?

Can anybody help me understand this?

Thanks.