The Fundamental Theorem of Calculus part 1 (part iii)
So, we are now ready to prove the FTC part 1. We're going to follow the proof in Stewart and add in some discussion as we go along to motivate what we are doing. What we are going to prove is that: $latex \frac{d}{dx} \int_a^x f(t) dt=f(x)$ for $latex x\in $ when $latex f$ is continuous on