Let \( f(x)=\left\{\begin{array}{ll}2 x+1, & \text { when } 1 \leq ...

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Let \( f(x)=\left\{\begin{array}{ll}2 x+1, & \text { when } 1 \leq x \leq 2 \\ x^{2}+1, & \text { when } 2 \leq x \leq 3\end{array}\right. \)
Show that \( \int_{1}^{3} f(x) d x=\frac{34}{3} \)
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