Puzzled with how to answer

Question

If ∫5to1 f(x)dx=8 and ∫5to3f(x)dx=5.2, find ∫3to1 f(x)dx

Answer 1

First of all, you might want to get into the habit of declaring your integrals from left to right ( "integral from 1 to 5" instead of "... 5 to 1", since int(5,1) = -int(1,5)

Next, recall that ∫a to c f(x)dx = F(c) - F(a), and ∫b to c f(x)dx = F(c) - F(b), and ∫a to b f(x)dx = F(b) - F(a).

This, in conjunction with the area addition principle leads to F(c) - F(a) = [F(b) - F(a)] + [F(c) - F(b)]

Therefore, just subtract [int(1,5)f(x)dx] - [int(1,3)f(x)dx] to give you your answer