The i th subinterval is given by

$[$a$+($i$-1)($b$-$a$)/($n$),$a$+$i$($b$-$a$)/($n$)].$

Evaluate

$\backslash$int$\_0^1$ x$^(3)$dx

using upper and lower sums. HINT:

b$^(4)-$a$^(4)=($b$^(3)+$b$^(2)$a$+$ba$^(2)+$a$^(3))($b$-$a$)$