**Homework for 5.2** 1. The graph of \( f \) consists of two straight lines and a semicircle over the interval \([-2, 10]\). Use it to evaluate each of the following: - (a) \( \int_{-2}^{1} f(x) \, dx \) - (b) \( \int_{-1}^{7} f(x) \, dx \) - (c) \( \int_{-2}^{10} f(x) \, dx \) **Graph Explanation:** - The graph contains a semicircle centered at \( x = 4 \) with a radius extending from \( x = 2 \) to \( x = 6 \). The semicircle is drawn above the x-axis. - A straight line starts from the interval \([-2, 0]\) with a positive slope, intersecting the x-axis at \( x = -2 \). - Another straight line begins from the point \( x = 6 \) and extends to \( x = 10 \), also having a positive slope. - The region under the curve is partially shaded from \( x = 0 \) to \( x = 5 \) beneath the semicircle. Each integral request asks for the area calculation of the function \( f(x) \) over specified intervals provided in the problem statement.

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