The first fundamental theorem of calculus states that if f is continuous on the closed interval [a, b] and F is the antiderivative (indefinite integral) of f on [a, b], then integral_a^bf(x)dx = F(b) - F(a).
status | proved proof date | 1668 (357 years ago) provers | James Gregory | Isaac Barrow additional people involved | Gottfried Leibniz | Isaac Newton
integral_a^bf(x)dx = ( integral f(x)dx/.x->b) - ( integral f(x)dx/.x->a)
