Integration 

Integration is the inverse of differentiation, and it is needed to solve differential equations.
Integrating a curve (or line) $y=f(x)$ with respect to $x$ between two limits (say, $x={\alpha}$ and $x={\beta}$ ) will give the area enclosed by the curve (or line), the xaxis and the lines $x={\alpha}$ and $x={\beta}.$ If a curve (or line) exists both above and below the xaxis between the limits ${\alpha}$ and ${\beta},$ the regions above and below the xaxis must be integrated separately and then summed to find the magnitude of the area.
The general rule for integration of power functions is shown below: