\int{ydx}=\int{b\sin{t}(-a\sin{t})dt}=-ab\int{\sin^2{t}}dt=-ab\int{\frac{1-\cos{2t}}{2}}dt=\frac{-ab}{2}\int{(1-\cos{2t})}dt=-\frac{ab}{2}(t-\frac{\sin{2t}}{2})=\frac{ab}{4}(\sin{2t}-2t)