5.3 The Fundamental Theorem of Calculus/41

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \int \limits _{0}^{\pi }f(x)dx\quad {\text{where}}\;f(x)={\begin{cases}sin(x)&0\leq x<{\frac {\pi }{2}}\\cos(x)&{\frac {\pi }{2}}\leq x\leq \pi \end{cases}}\int \limits _{0}^{\frac {pi}{2}}f(x)dx}