kill(all)$ reset()$

x(t):=cos(t)^4;
y(t):=sin(t)^4;

dx:diff(x(t),t);

dy:diff(y(t),t);

I:'integrate(x(t)*dy-y(t)*dx,t,0,%pi/2);

I, integrate;

wxplot2d([parametric,x(t),y(t),[t,0,%pi]]);