In simple words..
1)Differentiation helps to find the slope of any given curve at any given point.It helps to understand the behaviour af any curve and also gives information about its continuity,It helps to know the number the number of solutions of a given curve(i.e the points where it cuts the x-axis).We also getto know the maxima and minima of a function.
2)Integration helps to calculate the area under a curve w.r.t to either the x or y axis within two limits (definite integration) or under the whole curve(indefinite integration).