The first set of axes below shows the graph of $y = {\text{ }}f(x)$ for $- 4 \leqslant x \leqslant 4$.

Let $g(x) = \int_{ - 4}^x {f(t){\text{d}}t}$ for $- 4 \leqslant x \leqslant 4$.

(a)     State the value of x at which $g(x)$ is a minimum.

(b)     On the second set of axes, sketch the graph of $y = g(x)$.

(a)     $x = 1$     A1

[1 mark]

(b)     A1 for point (–4, 0)

A1 for (0, − 4)

A1 for min at $x = 1$ in approximately the correct place

A1 for (4, 0)

A1 for shape including continuity at $x = 0$

[5 marks]

Total [6 marks]