The derivative of the definite integral of a function with respect to its upper limit is the original function evaluated at that upper limit.

The definite integral of a function from a to b is the difference between the antiderivative evaluated at b and the antiderivative evaluated at a.

Differentiation and integration are inverse operations; one can 'undo' the other.

$g(x) = \int_{a}^{x} f(t) dt \implies g'(x) = f(x)$

$\int_{a}^{b} f(x) dx = F(b) - F(a)$, where F is the antiderivative of f.

1. Find the antiderivative F(x) of f(x). 2. Evaluate F(b) and F(a). 3. Subtract F(a) from F(b): F(b) - F(a).

Apply FTOC Part 1: $g'(x) = f(x)$.

The constant of integration cancels out when evaluating F(b) - F(a), so it's not necessary to include it.

Apply FTOC Part 1 and the chain rule: $g'(x) = f(h(x)) * h'(x)$