(1 point) The area A of the region S that lies under the graph of the continuous function f on the interval a, b is the limitof the sum of the areas of approximating rectangles: A=\lim _{n \rightarrow \infty}\left[f\left(x_{1}\right) \Delta x+f\left(x_{2}\right) \Delta x+\ldots+f\left(x_{n}\right) \Delta x\right]=\lim _{n \rightarrow \infty} \sum_{i=1}^{n} f\left(x_{i}\right) \Delta x \text { where } \Delta x=\frac{b-a}{n} \text { and } x_{i}=a+i \Delta x The expression A=\lim _{n \rightarrow \infty} \sum_{i=1}^{n} \frac{\pi}{4 n} \tan \left(\frac{i \pi}{4 n}\right)

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