Integration by substitution, why do we change the limits? I've highlighted the part I don't understand in red. Why do we change the limits of integration here? What difference does it make?

Source of Quotation: Calculus: Early Transcendentals, 7th Edition, James Stewart

The original limits is for variable $x$, and the new limits is for the new variable $u$. If you can get a primitive function 
$$\frac{8}{27}(1+\frac{9}{4}x)^\frac{3}{2}$$
by observation, it is unnecessary.
