Question 1195869
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I'll just put them in words:

  I. If there is a finite area between an upper non-negative curve and 
     the x-axis, is there also a finite area between a lower non-negative 
     curve and the x-axis?

 II.  Take the special case. If f(x)=1 then does {{{int(1,dx,0,infinity)}}} exist?

III. This is the same as I.  If there is a finite area between an upper 
     non-negative curve and the x-axis, is there also a finite area between
      a lower non-negative curve and the x-axis?

 IV. If there is a finite area between a lower non-negative curve and 
     the x-axis, is there also a finite area between an upper curve and the 
     x-axis?

Edwin</pre>