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**hatsoff** Okay, so clearly $\displaystyle \underline{\int_0^1}f\;dx=0$ (since $\displaystyle m_i=0$), so we can concentrate on $\displaystyle \overline{\int_0^1}f\;dx$.

The problem is, I am having trouble interpreting my textbook on how to calculate this. According to it,

$\displaystyle \overline{\int_0^1}f\;dx=\inf\{U(P,f)$ : $\displaystyle P$ a partition of $\displaystyle [a,b]\}$.

Okay, that's all very well. But how in the world do we compute that? Thus far, I have not been able to find a way.

Any help would be much appreciated. Thanks!