Area of the region bounded by the curve $y=\cos x$ between $x=0, x=\pi$ and x-axis is:

2 sq. units

y = cos x        x = 0,  x = π  x axis

x = 0

from x = 0 to $\frac{\pi}{2}$ graphis pasitive ⇒ postitive area

from $x=\frac{\pi}{2}$ to $\pi$ graph is negative ⇒ negative area

so area = $\int\limits_0^{\frac{\pi}{2}} \cos x d x+\left(-\int\limits_{\frac{\pi}{2}}^\pi \cos x d x\right)$

-ve sign to counter -ve area

$=[\sin x]_0^{\frac{\pi}{2}}+[-\sin x]_{\frac{\pi}{2}}^\pi$

$1-0+[-0+1]$

$=1+1=2$

area = 2 sq. units