[tex]x^3[/tex] is strictly increasing on [0, 5], so
[tex]\max\{x^3 \mid 0\le x\le5\} = 5^3 = 125[/tex]
and
[tex]\min\{x^3 \mid 0 \le x\le5\} = 0^3 = 0[/tex]
so the integral is bounded between
[tex]\displaystyle \boxed{0} \le \int_0^5x^3\,dx \le \boxed{125}[/tex]
