5.3 The Fundamental Theorem of Calculus/41

$\int \limits _{0}^{\pi }f(x)dx\quad {\text{where}}\;f(x)={\begin{cases}sin(x)&0\leq x<{\frac {\pi }{2}}\\cos(x)&{\frac {\pi }{2}}\leq x\leq \pi \end{cases}}$

Failed to parse (syntax error): {\displaystyle = \int\limits_{0}^{\frac{\pi}{2}}f(x)dx + \int\limits_{\frac{\pi}{2}}^{\pi}f(x)dx = \int\limits_{0}^{\frac{\pi}{2}}\sin(x)dx + \int\limits_{\frac{\pi}{2}}^{\pi}\cos(x)dx \\[2ex] &= -\cos(x)\\[2ex] }