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Piecewise function integrated thrice


Why can't Mathematica integrate thrice a piecewise defined function? 
Here is what I mean:

This is a step function:
h[x_]:ÿ[x>0,1,0]
It can (of course) be plotted and integrated. Then let:
f[x_]:ÿtegrate[h[t],{t,0,x}]
f, as well as h, can be plotted and if I put
g[x_]:ÿtegrate[f[t],{t,0,x}]
then g can be plotted, but any integral (definite or not) that I attempt
to compute about g leads to an error message (though g can be 
NIntegrated).

Am I doing something wrong somewhere? Thanks for any help.

Regards,

Daniel CLEMENT



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