integrals help please!?

Question

Let f be a continuous function on the closed interval of [0,2]. If 2 < or equal to f(x)< or equal to 4, then the greatest possible value of the integral of f(x)dx from 0 to 2 is

0,2,4,8, or 16

the answer is 8 but i don't get how they get that answer.

please and thank you!

Answer 1

Since the largest number f(x) can equal is 4, integrate 4 from 0 to 2.

Which is 4x evaluated from 2 to 0
4(2) - 4(0) = 8

Answer 2

The best case is if f(x) =4 for all x.So the integral of this constant is 4*2 (2 length of the interval)=8