How do you use the Fundamental Theorem of Calculus to evaluate an integral?
If we can find the antiderivative function
We are usually given continuous functions, but if you want to be rigorous in your solutions, you should state that
FTC part 2 is a very powerful statement. Recall in the previous chapters, the definite integral was calculated from areas under the curve using Riemann sums. FTC part 2 just throws that all away. We just have to find the antiderivative and evaluate at the bounds! This is a lot less work.
For most students, the proof does give any intuition of why this works or is true. But let's look at