The area which is located under the curve gives us the angle in radians; we divide this by 2π to get units in revs (revolutions).
So for 0 ≤ t ≤ 2,
number of revs = 20rad/s * 2s * 1rev/2π rads = 6.37 revs
So for 2 ≤ t ≤ 3.9,
number of revs = 10rad/s * 1.9s * 1rev/2πrads = 3.02 revs
Therefore the total is about:
6.37 revs + 3.02 revs = 9.39 revs ≈ 9.4 revs