Area of the region bounded by the curve y = cos x between x = 0 and x = π is

The correct option is 2 sq. units.

To find the area of the region bounded by the curve $y=\cos x$ between $x=0$ and $x=\pi$, we must consider the behavior of the cosine function over this interval.

The function $y=\cos x$ is positive in the interval $[0,\frac{\pi }{2}]$ and negative in the interval $[\frac{\pi }{2},\pi ]$.
Since area is a physical quantity and must always be positive, we calculate the total area by taking the absolute value of the integral in the region where the curve lies below the x-axis.

Therefore, the total area $A$ is given by the sum of two separate integrals:
$$A={\int }_0^{\frac{\pi }{2}}\cos x dx+|{\int }_{\frac{\pi }{2}}^{\pi }\cos x dx|$$

Let's evaluate the two integrals step-by-step.
The antiderivative of $\cos x$ is $\sin x$.

For the first part:
$${\int }_0^{\frac{\pi }{2}}\cos x dx={[\sin x]}_0^{\frac{\pi }{2}}=\sin \left(\frac{\pi }{2}\right)-\sin \left(0\right)=1-0=1$$

For the second part:
$${\int }_{\frac{\pi }{2}}^{\pi }\cos x dx={[\sin x]}_{\frac{\pi }{2}}^{\pi }=\sin \left(\pi \right)-\sin \left(\frac{\pi }{2}\right)=0-1=-1$$

Taking the absolute value for the second region to represent area:
$$|-1|=1$$

Adding the two values together:
$$A=1+1=2\text{sq. units}$$

Thus, the area of the bounded region is 2 sq. units.