Suppose that \(f\) is the function given in Figure 5.2.2 and that \(f\) is a piecewise function whose parts are either portions of lines or portions of circles, as pictured.
Sketch a precise graph of \(y = A(x)\) on the axes at right that accurately reflects where \(A\) is increasing and decreasing, where \(A\) is concave up and concave down, and the exact values of \(A\) at \(x = 0, 1, \ldots, 7\text{.}\)
With as little additional work as possible, sketch precise graphs of the functions \(B(x) = \int_3^x f(t) \, dt\) and \(C(x) = \int_1^x f(t) \, dt\text{.}\) Justify your results with at least one sentence of explanation.
