Integrate the systems

> x1a:=int(+1,s=0..t);
x1b:=eval(x1a,t=sw)+int(-1,t=sw..tau):
x1b:=subs(tau=t,x1b);
y1:=eval(x1b,t=1);
display([
plot(x1a,t=0..1,color=blue),
seq(plot(x1b,t=sw..1,color=red),
sw=[seq(k/10,k=1..10)])],
thickness=2);

> x11a:=int(x1a,t=0..tau):
x11a:=subs(tau=t,x11a);
x11b:=eval(x11a,t=sw)+int(x1b,t=sw..tau):
x11b:=subs(tau=t,x11b);
y11:=eval(x11b,t=1);
display([
plot(x11a,t=0..1,color=blue),
seq(plot(x11b,t=sw..1,color=red),
sw=[seq(k/10,k=1..10)])],
thickness=2);

> x2a:=int(x1a^2,t=0..tau):
x2a:=subs(tau=t,x2a);
x2b:=eval(x2a,t=sw)+int(x1b^2,t=sw..tau):
x2b:=subs(tau=t,x2b);
y2:=eval(x2b,t=1);
display([
plot(x2a,t=0..1,color=blue),
seq(plot(x2b,t=sw..1,color=red),
sw=[seq(k/10,k=1..10)])],
thickness=2);

>