Fundamental Theorem of Calculus (Part I)

For Tutorial 2 Q3, we are actually using Part 1 of the Fundamental Theorem of Calculus, which states that $\displaystyle\frac{d}{dx}\int_a^x f(t)\,dt=f(x)$ for a continuous function $f$ .

If the upper limit is a function $g(x)$ instead, we have $\Large\displaystyle\boxed{\frac{d}{dx}\int_a^{g(x)}f(t)\,dt=f(g(x))g'(x)}$ by the chain rule. This is the formula that is going to be useful for Q3.