If int{x=1 to x=3} (3f(x)+8) dx=14, then int{x=1 to x=3} f(x)dx = ?

Question

If ∫₁³ (3f(x)+8) dx=14, then ∫₁³ f(x)dx =

Answer 1

∫_{(1 to 3)} [3f(x) + 8]dx = 14

3 ∫_{(1 to 3)}f(x)dx + 8∫_{(1 to 3)}dx = 14

3 ∫_{(1 to 3)}f(x)dx = 14 - 16

So, ∫_{(1 to 3)}f(x)dx = -2/3