Integration is the inverse process to differentiation. Some people call it anti-differentiation.
Instead of multiplying the power at the front and subtracting one from the power, we add one to the power and then divide by the new power.
This just means, integrate with respect to . Remember, add one to the power and divide by the new power.
The appears because when you differentiate a constant term, the answer is zero, so as we are performing 'anti-differentiation', we presume there may have been a constant term, which reduced to zero when differentiated. This is called the constant of integration.
Similar rules apply to integration whereby we need to remove the brackets first as the expression has to be sums and/or differences of terms of the form .