This code works normally:

documentclass[pstricks]{standalone}

usepackage{pst-plot}

%usepackage{auto-pst-pdf}% only for pdflatex

begin{pspicture}[algebraic,linestyle=curve](-2,-6)(6,6)

psaxes{->}(0,0)(-2,-4)(5.5,4)[$x$,0][$y$,90]

psclip{%

    psplot[linestyle=none]{0}{6.5}{x*(3-x)/2}}

psplot[linecolor=blue,fillstyle=vlines]{.5}{5}{x*(x-6)+6}

endpsclip

psplot{0}{4.5}{x*(3-x)/2}}

psplot[linecolor=blue]{.5}{5}{x*(x-6)+6}

rput[bl](1.8,1.2){$y=dfrac{-x^2+3x}{2}$}

rput[t](2,-3.1){$y=x^2-6x+6$}

end{pspicture}

end{document}

but the following code is not working:

documentclass[pstricks]{standalone}

usepackage{pst-plot}

%usepackage{auto-pst-pdf}% only for pdflatex

begin{pspicture}[algebraic,linestyle=curve](-2,-6)(6,6)

psaxes{->}(0,0)(-2,-4)(5.5,4)[$x$,0][$y$,90]

psclip{%

    psplot[linecolor=blue,]{-1}{5}{-1*x+2}}

    psplot[fillstyle=hlines]{.5}{5}{x*(x-6)+6}

endpsclip

psplot[linewidth=1.5pt]{.5}{5}{x*(x-6)+6}

rput[bl](1.5,1){$y=-x+2$}

rput[t](2,-3.1){$y=x^2-6x+6$}

end{pspicture}

end{document}

You have to define an area which will then be clipped. The area is build with connecting the first point with the last one. For a line you simply get an area of zero, and from this area nothing can be clipped!

With psline(0,2)(5,-3)(0,-3) I define a triangle. It is automatically a closed area becasue it draws a line from (0,-3) to (0,2).
And from that area the curve with {x*(x-6)+6} is clipping a part which will be filled.

documentclass[pstricks]{standalone}

usepackage{pst-plot}

begin{document}



begin{pspicture}[algebraic,plotstyle=curve](-2,-6)(6,6)

psaxes{->}(0,0)(-2,-4)(5.5,4)[$x$,0][$y$,90]

psclip{psline[linestyle=none](0,2)(5,-3)(0,-3)}

   psplot[fillstyle=vlines]{.5}{5}{x*(x-6)+6}

endpsclip

psplot[linewidth=1.5pt,linecolor=blue]{.5}{5}{x*(x-6)+6}

psline[linewidth=1.5pt](0,2)(5,-3)

rput[bl](1.5,1){$y=-x+2$}

rput[t](2,-3.1){$y=x^2-6x+6$}

end{pspicture}



end{document}

As an alternative you can calculate the intersectionpoints (needs package pst-intersect) and using pscustom

%%usepackage{pst-intersect} in the preamble

begin{pspicture}[algebraic](-2,-6)(6,6)

pssavepath[linewidth=1.5pt]{Curve}{psplot{.5}{5}{x*(x-6)+6}}

pssavepath[linewidth=1.5pt]{Line}{psplot{0}{5}{-x+2}}

psintersect[name=C]{Curve}{Line}

psaxes{->}(0,0)(-2,-4)(5.5,4)[$x$,0][$y$,90]

pscustom[fillcolor=red,fillstyle=solid,opacity=0.4]{%

  psplot{psGetNodeCenter{C1}C1.x}{psGetNodeCenter{C2}C2.x}{x*(x-6)+6}%

}

end{pspicture}

However, that one with pst-intersect works not with xelatex

Generic Template

Proposed features:

• functions are defined globally so you can change easily.


• intersection points are calculated at "runtime" as opposed to statically hard coded.

documentclass[pstricks,border=12pt]{standalone}

usepackage{pst-eucl,pst-plot}





deff(#1){((#1)^2-6*(#1)+6)}

defg(#1){(2-(#1))}



begin{document}

begin{pspicture}[algebraic,saveNodeCoors,PointSymbol=none,PointName=none](-1,-3.5)(6,4)

    psaxes{->}(0,0)(-.5,-3.5)(5.5,3.5)[$x$,0][$y$,90]

    pstInterFF{f(x)}{g(x)}{0}{A}

    pstInterFF{f(x)}{g(x)}{5}{B}

    pscustom*[linecolor=yellow!50]{%

        psplot{N-A.x}{N-B.x}{f(x)}

        psplot{N-B.x}{N-A.x}{g(x)}

        closepath

    }

    psset{linewidth=2pt,linecolor=cyan}

    psplot{.5}{5}{f(x)}

    psplot{-.5}{5}{g(x)}

    uput[-90](*5 {g(x)}){$y=-x+2$}

    uput[45](*.7 {f(x)}){$y=x^2-6x+6$}

end{pspicture}

end{document}

Statically hard-coded Version

Cons: you have to calculate the intersection points in advance by hands.

documentclass[pstricks,border=12pt]{standalone}

usepackage{pst-plot}



deff{x^2-6*x+6}

defg{2-x}



begin{document}

begin{pspicture}[algebraic](-1,-3.5)(6,4)

    psaxes{->}(0,0)(-.5,-3.5)(5.5,3.5)[$x$,0][$y$,90]

    pscustom[fillstyle=vlines,hatchcolor=red,hatchsep=0.8pt]{psplot{1}{4}{f}psplot{4}{1}{g}}

    psset{linewidth=2pt,linecolor=blue}

    psplot{.5}{5}{f}

    psplot{-.5}{5}{g}

    uput[-90](*5 {g}){$y=-x+2$}

    uput[45](*.7 {f}){$y=x^2-6x+6$}

end{pspicture}

end{document}