I discovered quite by accident while watching the Schoolhouse Rock video on adjectives that the Fundamental Theorem of Calculus is used to solve an integral!
This screenshot is from 1:30 in the video, which can be found here.
As happy as I was to see an integral appear, I'm not sure how I feel about the context. As I said before, the show was about adjectives. Initially, the girl who is assigning adjectives throughout gives the kid on the left the adjective dumb and the one on the right brainy.
Naturally this makes the left kid sad and the right kid happy. But then the kid on the left is the one that works out the integral above. The girl then swaps their adjectives.
All is right with the world? Well sort of. I hate the fact that they are using math in this way to sort kids into brainy and dumb. Too many students feel already that they are not math people, and while I know the original writers of the video were trying to subvert stereotypes about who knows what, at the end of the day we have one kid who is literally labelled dumb based on his math ability.
This song was one of the first Schoolhouse Rock's that were written, and first aired on March 2, 1974 as part of the "Grammar Rock" videos. It's intriguing to me because it represents first steps: trying to move past harmful categorizing, but doesn't quite make it all the way.