Subjects/Calculus II/Definite integral and Fundamental Theorem of Calculus/Fundamental Theorem of CalculusSection 3.3Fundamental Theorem of CalculusPart I. If f is continuous andFormulaCopy LaTeXG(x)=∫axf(t)dt,View detail →thenFormulaCopy LaTeXG′(x)=f(x).View detail →More generally, by the chain rule:Copy LaTeXdxd∫ag(x)f(t)dt=f(g(x))g′(x).View detail →With both limits variable:Copy LaTeXdxd∫u(x)v(x)f(t)dt=f(v(x))v′(x)−f(u(x))u′(x).View detail →Part II. If F′(x)=f(x), thenFormulaCopy LaTeX∫abf(x)dx=F(b)−F(a).View detail →