Question

What is a integration?

Answer 1

In differentiation, you study the effect of a small change in independent variation on dependent variation $(\frac{dy}{dx}$ as dx $\to$ 0). For example when function $f\left(x\right)=x^2$ is differentiated you get 2x. This means that at any point in the curve of $f\left(x\right)=x^2$, the slope of tangent to the curve is 2x.
In integration, you study the effect of all small changes and sum them up. In other words, integration of y = 2x will be $x^2$. However, you add a constant of integration. Hence integration of $2x=x^2+c$. Why ? If you differentiated $x^2+c$ you will get 2x only as differentiation of constant = 0.
Integration also is used to calculate area under the curve and x - axis.