Must be positive?

[runic mortar]

About the problem at 5:13 on https://www.khanacademy.org/math/ap-calculus-ab/ab-integration-new/ab-6-5/v/interpreting-behavior-of-antiderivative , notice the tab transcript, and screenshot attached. I have a hard time understanding. I thought integral were about change and not quantity. Does the problem mean a positive change or positive value, of whatever quantity is changing? If the latter, I fail to understand the host explanation about how the quantity must be positive.

Although if negative quantity is possible, I'm assuming it's one that can be, eg temperature.

[neon sonnet]

The integral over a range is the total area under the curve in that range.

The integral of velocity is position. The longer you travel at higher speeds, the farther you've gone. If you stop traveling and your velocity is zero, you've still travelled a bunch and your position can still be large and positive.

I'm not watching the video on my phone though, so my apologies if that's not what you're asking.