\frac{1}{4}P=\int_{0}^{a}ydx=\frac{ab}{4}(\sin{2t}-2t)|^{0}_{\frac{\pi}{2}}=\frac{ab}{4}(\sin{0}-2\cdot{0})-\frac{ab}{4}(\sin{\pi}-\pi)=\frac{ab\pi}{4}