Integral calculus quiz

The diagram shows the graph of y = f( x ) with intercepts at x = −1, 0, 3 and 4.

A trigonometric function f( x ) satisfies the condition

Evaluate:

The shaded region is enclosed by the curve y = x^3 − 7x and the line y = 2x, as shown in the diagram. The line y = 2x meets the curve y = x3 − 7x at O(0, 0) and A(3, 6). Do NOT prove this.