What is the answer to this integral problem?

Question

If ∫₀² f(x) dx = 15, ∫₂³ f(x) dx = 12, and ∫₀³ g(x)+5 dx = 10, then what is ∫₀³ 2f(x) - 3g(x) dx?

Answer 1

∫₀³ f(x)dx = 15 +12 = 27

∫₀³ g(x) + 5 dx = ∫₀³ g(x) dx + 15 = 10 so ... ∫₀³ g(x)dx = -5

∫₀³ 2f(x) - 3g(x) dx = 2 ∫₀³ f(x)dx - 3 ∫₀³ g(x)dx = 2·27 - 3(-5) = 69