Question: Simplifying expressions(symbolic integration)

Hi all,

I have the following functions.

restart:
with(IntegrationTools):
N:=4:

i:='i':
for i from 1 to N do
    assume(x[i-1]::constant):
    assume(x[i+1]::constant):
    assume(x[i-1]::constant):
    assume(h::constant):

 phi[i](t):=piecewise(t>=x[i-1] and x[i]>t, (t-x[i])/(h), x[i]

(x[i+1]-t)/(h), 0);

end do;

## my goal is solve the integrals involving phi[i]'s as integrand and x[i]'s as its limits.

## as a test case I tried to calculate Int( diff( phi[1], t)* diff( phi[1], t), t=x[0]..x[2]);

V:=Int(diff(phi[1](t), t)*diff(phi[1](t), t), t=x[0]..x[2]);

addionally assuming(x[0]<x[1] and x[1]<x[2]

 and x[2]<x[3]);

Parts(V, phi[1]);

## The output pretty much looks what we get by hand, but there are plently

 of Heaviside functions involve. 

By a simple look at the output those Heaviside functions have to

 disappear by using the order x[0]>x[1]>x[2].

But it isnt. 

Would any body please point out my mistake or give me some better idea?

Thanks!!!