Activity 5.2.2. 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. Figure 5.2.2: At left, the graph of y = f(.'t'). At right, axes for sketching y = ALT). In addition, let A be the function dened by the rule A(.r) : j: f(t) (it. a. What does the Second FTC tell us about the relationship between A and f? b. Compute [1(1) and A( 3) exactly. c. Sketch a precise graph of y : A(x) on the axes at right that accurately reects where A is increasing and decreasing, where A is concave up and concave down, and the exact values ofA at x = O, 1, . . . , 7. d. How is A similar to, but different from, the function F that you found in Activity 5.1.2? e. With as little additional work as possible, sketch precise graphs of the functions BLT) : f; f (t) (it and C(x) : ff _f(t) dt. ]ustify your results with at least one sentence of explanation