Integral China Intermediate

Problem - 4601

Let $$f(x)=\left\{\begin{array}{ll} \cos{x} &, x\in[-\frac{\pi}{2}, 0)\\e^x&,x\in[0,1] \end{array}\right.$$

Compute $\displaystyle\int_{-\frac{\pi}{2}}^{1}f(x)dx$.

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