Certain Limits can be evaluated by using a method known as limit as a sum. Transforming a limit question to integration makes it easy to solve. Sometimes, it is only possible way to solve a question. The method is explained in the image.
Note that above result is only true when limit is infinity. Also, integration not always go from 0 to 1. Again it depends on Limit. If summation is ending at 2x where x-> (infinity), integration is from 0 to 2. (Why so?). If you can't point out why, Mention in comments and I will answer.
However, lower limit is always zero given that summation starts from a finite value.
Since I don't know how to use Latex or how to insert image in middle of text, I am using image to explain it all. Can someone tell me how to write in Latex and insert images in between text.