Step 1: Ensure that the lower bound of your antiderivative is a constant, a , and the upper bound is an equation, x .
Step 2: Take the derivative of your antiderivative.
At this point you essentially cancel out the antiderivative and plug your upper bound equation , x , into the equation that was inside the antiderivative, .
i)
ii)
iii)
iv)
You really want to be able to get from (i) to (iv) without applying (ii) and (iii). Those middle steps are there just to show you how one truly gets from (i) to (iv).
Step 3 (only if your equation is more than just an x ): If the upper bound is more than just a basic x , then you will need to multiply the equation you created in Step 2 , , by the derivative of the upper bound.
Since the upper bound in this situation is more than just the standard, x , you are essentially performing a Chain Rule . This means you will need to multiply your result from Step 2, , by the derivative of the upper bound. In this example the derivative of sin(x) would be cos(x) . You would multiply by cos(x) .