What's the difference between VerticalBar and VerticalLine?

I copy the "lim" command in the Help,it seems doesn't work easily,what should I do make it work,

how to plot the second picture,for the area is that with abs

z1 := -3*i*(2+i)*(3+2*i)*(1+4*i)

zz1 := expand(z1)

zz1 := -18*i-93*i^2-90*i^3-24*i^4

(3)  subs(i^2 = -1, i^3 = -i, i^4 = 1, zz1)=72*i+69

(4)  subs(i^2 = -1, zz1)=-18*i+93-90*i^3-24*i^4    

I don't like the way in (3) to get my answer.Are there some easy ways?

for example:this equation:(1 - 2 x y[x]) y'[x] == x^2 + (y[x])^2 - 2

and how to make the solution in this form:

y=（x^3）/3+x*(-2+y^2)+C

not the form y=f(x)