Why calculus and not straight to analysis?

Keep in mind that I have not took an analysis course.

Ok, there is calculus, where you learn about derivatives, integrals, and infinite series.  If you are lucky, you get into higher dimensions. 

With real analysis, there are some delta-epsilon proofs and proving stuff like L'hopital's rule, which you just learned to use it.  But of course that is just baby analysis. 

In analysis, you first learn about measures, like Lebesgue measure and lebesgue-stieltjes measures.  Also integration theory.  With this, you can integrate a much larger range of functions then the ones you see in calculus.  Then you can get into functional analysis, but I haven't gotten that far, yet.  I am more of an algebra person and topology person.