Given that y = sin x - 1 / 2,
first sub y = 0
sin x = 1 / 2
x = pi / 6 or 5pi / 6
From the graph, you know that A ( 5pi / 6, 0 )
The height of AB:
0 - [ sin ( 3pi / 2 ) - 1/2 ]
= 3 / 2
Therefore the area of ABCD:
( 2pi - 5pi / 6 )( 3 / 2 )
= 7pi / 4 sqr. units