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$\frac 12 \int_{0}^{1} x^4(1-x)^4 dx\leq \int_{0}^{1}\frac{x^4(1-x)^4}{1+x^2}dx \leq \int_{0}^{1} x^4(1-x)^4dx$

This is my homework assignment whereby I have no idea of how should i get started. Could i have some hint on this question??

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    Hint: if $0 \leq x \leq 1$, then $1/2 \leq 1/(1+x^2) \leq 1$. Now look at the areas that these integrals represent.2012-11-15
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    hmm... I still don't get it, @OldJohn2012-11-15

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