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I recently came across the terms: 'upper Riemann sum' and 'lower riemann sum'. Are they represent the same things as of 'upper sum' and 'lower sum' defined as follows.

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    For reference see books of Calculus and Analisys of Serge Lang. For exemple p. 296 of http://books.google.com.br/books?id=xNipwIAOq2EC&pg=PR13&lpg=PR2&dq=Serge+Lang+calculus&hl=pt-BR2012-12-21

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Yes. The upper Riemann Sum of $f$ with respect to $\mathcal{P}$ is defined as \begin{equation} U_{f,\mathcal{P}}:=\sum\limits_{i=1}^{n}{c_i\left( x_i-x_{i-1} \right)} \end{equation} while the lower Riemann sum of $f$ with respect to $\mathcal{P}$ is defined as \begin{equation} L_{f,\mathcal{P}}:=\sum\limits_{i=1}^{n}{d_i\left( x_i-x_{i-1} \right)} \end{equation} where $c_i,d_i$ are the supremum and infimum of $f$ in $[x_{i-1},x_i]$

We can then define the upper and lower Riemann integrals of $f$ as the unique real numbers \begin{equation} \overline{\int\limits_{a}^{b}}f:=\inf_{\mathcal{P}}U_{f,\mathcal{P}}=\inf \left\{ U_{f,\mathcal{P}}:\mathcal{P}\text{ is a partition of }\left[ a,b \right]\right\} \end{equation} and \begin{equation} \underline{\int\limits_{a}^{b}}f:=\sup_{\mathcal{Q}}L_{f,\mathcal{Q}}=\sup \left\{ L_{f,\mathcal{Q}}: \mathcal{Q}\text{ is a partition of }\left[ a,b \right] \right\} \end{equation} Whenever the two coincide, your function is integrable