So I took a guess on this question and got it right but after multiple attempts to understand it, I still don't get why that was the right answer. Could you explain why the following is the case? I attempted to solve the following via integrations but my calculator got overloaded and I had to restart it.

I've been working on Calculus 2 content this past semester, and I'm excited to finally launch it. It includes most material covered in a second semester Calculus course and AP Calculus BC.
Please take a look and I hope you find the videos helpful.
https://www.bothellstemcoach.com/calculus-2-problem-solving