If F(x) satisfies F ’ (x) = f(x), and F(A) = 10, F(B) = 15, what is ʃ f(x)dx, if the limits of the integral are B (upper) and A (lower)?

Answer 1

Since F'(x) = f(x), F(x) is an antiderivative of f(x).

According to the Fundamental Theorem of Calculus, ∫_{(from A to B)} f(x)dx = F(B) - F(A) = 15 - 10 = 5.