Why is calculating the area under a curve required or rather what usage it would provide I understand Integration and Differentiation and see a lot of Physics / Electrical Theory using them.

Take for example a sine wave. So area for me means the space any object would occupy. So what's usage it comes to find the area of a sine curve? 

There are so a many formulas that calculates the area by Integration - but why calculation is required - I mean what information we can get (isn't it just space occupied) or rather what data we can find by calculating area of a curve via Integration?
The point is that in science and in real life, you come up against situations where you need to totalize or to aggregate or to accumulate some kind of growing quantity. Say you know how fast the snow is falling at any particular time, and want to know the accumulation after five hours. Say you have pollutants flowing into a lake at varying rates during the day or week, and want to know how much crud is in the lake after a few weeks. Both these examples are quantities that are accumulated from a varying contribution, and both are measured by an integral. And there’s no area in sight.
A function, differentiate it represent how fast it changes, integrate it represent how much change had accumulated. 

If we know the derivative of the function (how fast it changes), by integrate it, we find function itself. If we know how much change had accumulated, by differentiate it, we can find of the function of this thing.