From the given equations
sin x = cos x
At this interval, x = π/4.
The area will be,
A = ∫0π/4 cos x - sin x dx + ∫π/4π/2 sin x - cos x dx
= [sin x + cos x]0π/4 + [-cos x - sin x]π/4π/2
= (sin (π/4) + cos (π/4)) - (sin 0 + cos 0) + (-cos (π/2) - sin (π/2)) - (-cos (π/4) - sin (π/4))
= (√2/2 + √2/2) - (0+1) - (0+1) + (√2/2 + √2/2)
=2√2-2 = 0.828427.