Question

If the integral from a to b of f(x)dx=a+2b then integral from a to b of (f(x)+3)dx= ?

The answer: 5b-2a

How do I get to that answer??

Answer 1

integral of (f(x) + 3)dx = integral of f(x)dx + integral of 3dx

Answer 2

integral from a to b of (f(x)+3)dx
= integral from a to b of f(x)dx + 3(b-a)
= a + 2b +3b -3a
= 5b - 2a