Jasper is a Java library; any Java library can be used with any IDE, but that's not what one generally would call "integrate". That's why I asked what you meant by it. (And no, I wouldn't call what you wrote "detailed" by any stretch of the word).
There rarely is a "best" for anything. In this case I'd think that "best" would be defined by something like a combination of price and features, and only tangentially by how easy it is to develop with. Jasper is certainly one of the best free reporting packages for Java, but it's no match for something like Crystal Reports.