@PCMSE This is very difficult for me! I've been trying this for half an hour without too much success because I can't make out, by principle, how exactly this works. Drawing the parabola is ok, but I think integrating it is giving me a headache. I'll try again tomorrow.
@PCMSE Yes unfortunately it's been ages since I've done like the hard integration and so on. I'm getting some practice because I'm writing an answer that actually involves some computation, so maybe when I do that and get confident, I will sleep over it and get back to your question tomorrow. But I'm sure I can answer it!