Use Simpson's rule with 7 ordinates ( 6 strips) to find an approximation to \(\int _ { 0.5 } ^ { 2 } \frac { x } { 1 + x ^ { 3 } } \mathrm {~d} x\), giving your answer to three significant figures.
Find the exact value of \(\int _ { 0 } ^ { 1 } \frac { x ^ { 2 } } { 1 + x ^ { 3 } } \mathrm {~d} x\).