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We've done a lot of discussion of the concept of integrals of a function here on this blog. Their definitions and applications are so broad as to defy any one-sentence description, but one of the most basic is the idea of the area under a curve. More precisely it's the signed area under the curve - that is, the area above the x-axis is counted as positive and the area under counts as negative. Stealing the image from Wikipedia, which communicates the concept well:

Saw "Up" yesterday. How Pixar manages to be so consistent in their astonishing quality is entirely beyond me. In a bit of a tribute, this Sunday Function is not about any dramatically important special function, but instead it's about filling a balloon. Air or water, as your preference.

Let's start with a pretty simple function. It's not this week's official Sunday Function, but we'll use it to get there.