The Beauty of Integration

If you're thinking that this is an article on national integration then you are mistaken. Whether this article could teach you a couple of things on national integration, well that’s a different thing altogether. This article is to talk about integration in math – yes that same integration that most of us hated and few of us loved. That same integration that defined our math scores in our board exams and competitive exams. That same integration that didn’t make sense and made us wonder why (in today’s times we would say “Why this kolaveri di?”:))
In school, unfortunately integration is often introduced as the reverse process to differentiation. It has wide applications, for example in finding areas under curves and volumes of solids. But the fact is that integration is probably the sexiest thing in mathematics, just like temporary tables are in SQL. Integration, just like a catalyst in Chemistry lets you be a part of the process, create wonders and then leave taking all what you brought back with you.
In other words there's nothing to lose, but everything to gain. Though this may sound funny, strange and even unbelievable to many it is in simple words the truth and whole truth. If you don’t believe me let me tell you a story (or present a POC – Proof Of Concept :)) and I’m sure you’ll be left with your eyes wide open, mouths with jaws dropped and lost in thought wondering whether this is the same integration that scared the hell out of us.
Not so long ago in a far, far away land lived a man who had 3 children. This man had 17 horses and willed that after his death the horses be divided amongst his sons with the eldest getting half of the total, the 2nd getting 1/3rd and the youngest 1/9th. When the father died the sons sat and started the process of splitting the horses but were soon left in a tizzy. Dividing 17 horses in half meant the eldest would get 8 and half horses. How could one have half a horse? Not knowing what to do they asked all the village experts but none could solve their misery. Left with no option they sought divine intervention.
Finally one day a man with a horse appeared at their doorstep. The man had heard of their complicated case and offered to help them for a fee. The sons agreed and the man started. He added his horse to their tally making it a total of 18. From that he gave the eldest son his share of half that’s 9; the second 1/3rd that’s 6 and the youngest 1/9th that’s 2 totaling up to 9+6+2=17. The sons happy with the division gave the man his fee. The man calmly walked away happy not only with the reward but also his horse.   
I hope this convinces you that integration is nothing to be scared of but to be loved. In fact like all other problems it’s like a Bombay local train - looks filled to the max when it’s coming into the station but actually there are people just standing at the door while its empty inside.