Evaluate the integral. \[ \int_{0}^{\pi} f(x) d x \text { where } f(x)=\left\{\begin{array}{ll} \sin (x) & \text { if } 0 \leq x<\frac{\pi}{2} \\ \cos (x) & \text { if } \frac{\pi}{2} \leq x \leq \pi \end{array}\right. \]

Step 1 ：Given the function \(f(x)\) which is defined as \(\sin(x)\) for \(0 \leq x < \frac{\pi}{2}\) and \(\cos(x)\) for \(\frac{\pi}{2} \leq x \leq \pi\), we are asked to evaluate the integral of \(f(x)\) from 0 to \(\pi\).

Step 2 ：We can split the integral into two parts, one for each condition of the function. The first integral will be from 0 to \(\frac{\pi}{2}\) of \(\sin(x)\) and the second integral will be from \(\frac{\pi}{2}\) to \(\pi\) of \(\cos(x)\).

Step 3 ：The integral of \(\sin(x)\) from 0 to \(\frac{\pi}{2}\) is 1.

Step 4 ：The integral of \(\cos(x)\) from \(\frac{\pi}{2}\) to \(\pi\) is -1.

Step 5 ：Adding these two results together, we get a final integral of 0.

Step 6 ：Final Answer: \(\boxed{0}\)