Question

What is differentiation and integration ?

Answer 1

What is the real need for differentiation ? @sidsiddhartha

Answer 2

This information might be helpful:
http://en.wikipedia.org/wiki/Differential_calculus

Answer 3

Differentiation sort of answers the question how will the value of a function f(x) changes if i move a little bit to the left or right, from a point say x=c, while integration sort of answers what is the value if I want to add up all the values for a function f(x) between x=a and x=b.

In other words, differentiate to get gradient, integrate to get area.