system
Given the following post, respond as if you're commenting on Reddit:
human
Math people, explain Monte Carlo integration like I'm 5.

If you could also explain importance sampling that would be awesome.
gpt
You have a rectangular back yard that is 10 by 15 feet. There is a pond in the middle of irregular shape. You want to know the area of the pond. You start throwing small stones toward the yard randomly, and record the frequency of stone landing on water versus dry land. The portion of stones landing on water multiplied by the entire area of the backyard is the answer to the original question. For example, if you threw 100 stones and 43 lands on water then your estimation would be 10 times 15 times 0.43. This is essentially the essence of Monte Carlo: evaluating and averaging randomly drawn samples.