Given, curve y = cos x

and points x = 0 and x = 2π

It is clear from the graph that the required area is the three regions which are 

shaded. Clearly the curve ranges between 0 to π/2 in the I region, π/2 to 3π/2 in the

second region which is in the negative side of y-axis, and 3π/2 to 2π in the III region.

So, area of the shaded region A = ₀∫^π/2 y₁ dx + _π/2∫^3π/2 (-y₂ ) dx + _3π/2∫^2π y₃ dx 

=> A = ₀∫^π/2 cos x dx - _π/2∫^3π/2 cos x dx + _3π/2∫^2π cos x dx

=> A = [sin x ₀]^π/2 - [sin x _π/2]^3π/2 + [sin x _3π/2]^2π 

=> A = (sin π/2 - sin 0) - (sin 3π/2 - sin π/2) + (sin 2π - sin 3π/2)

=> A = (1 - 0) - (-1 - 1) + {0 - (-1)}

=> A = 1 + 2 + 1

=> A = 4 square units

So, the area is 4 square units