Let $ \displaystyle g(x) = \int^x_0 f(t) \,dt $, where $ f $ is the function whose graph is shown.
(a) Evaluate $ g(x) $ for $ x $ = 0, 1, 2, 3, 4, 5, and 6.
(b) Estimate $ g(7) $.
(c) Where does $ g $ have a maximum value? Where does it have a minimum value?
(d) Sketch a rough graph of $ g $.