Definition/Meaning  Word/Phrase 
branch of mathematics involving calculus and the theory of limits; sequences and series and integration and differentiation 
analysis

mathematics branch dealing with limits, differentiation and integration of functions of variables 
calculus

branch of mathematics that is concerned with limits and with the differentiation and integration of functions 
calculus
,
infinitesimal calculus

result of a mathematical integration; F(x) is the integral of f(x) if dF/dx 
integral

part of calculus that deals with integration and its application in the solution of differential equations and in determining areas or volumes etc. 
integral calculus
