Differential calculus is used to calculate the rate of change of a function with respect to a variable.
Eg let a function be f = xn Thus df/dx will give rate of change of f with respect of x.
df/dx = nxn-1
Integration on the other hand is a reverse process.
In this process we find the area under the curve of a function eg going on with the same function f if we integrate it from x = 1 to x = 2 then it will give us the area under the curve between the limits