Can the Integral of (1+x^3) be Bounded Between 2 and 6?

[armolinasf]

Homework Statement

Prove without computation that 2<Integral[0,2] (1+x^3)<6

The Attempt at a Solution

I know there is a theorem which says that if a function is bounded by two constants, then the integral of the function is also bounded by the integrals of the two functions. However, I'm not sure if that would apply. So how should I approach this one without computation? Thanks

 

[rock.freak667]

Here is a hint: the integral gives an area. Draw the graph in the given range.