examine the concept of the signed area function F(x)=∫ {from a to x} f(t)dt
apply the theorem F'(x)=d/dx ( ∫ {from a to x} f(t)dt)=f(x), and illustrate its proof geometrically
use the increments formula: δy≅dy/dx × δx to estimate the change in the dependent variable y resulting from changes in the independent variable x
develop the formula ∫ {from a to b} f(x)dx= F(b)−F(a) and use it to calculate definite integrals
