If f=f(x) is a function that is the derivative of F=F(x), so that F'(x)=f(x), we say that F is an anti-derivative of f. Anti-derivatives are connected to integration by the Fundamental Theorem of Calculus (FTC), which says that if F'(x)=f(x), then
In this discussion, we would like to do two things, use the FTC and anti-derivatives to find a numerical value for an area and analyze the behavior of an anti-derivative based on our knowledge of f.