# Integrate piecewise function with change of variable

I would like to integrate a piecewise defined function while operating a change of variable. I start by defining the function and another variable involved in the change of variable:

```
phi(x) = piecewise([([-1,1], (1-abs(x))*(1-abs(x))*(1+2*abs(x)))]);
phi(x) = phi.extension(0);
h=pi/n;
h=h.n();
```

What I would like to do is integrate the function `phi(x/h-1)`

between `0`

and `pi`

so I try it and results in

```
integral(phi(x/h-1),x,0,pi)
ValueError: substituting the piecewise variable must result in real number
```

So I then try to use another variable which I try to define to be 'real'

```
t=var('t')
assume(t,'real');
integral(phi(t/h-1),t,0,pi)
```

but it results in the same error... Now I try the "lambda" method since it worked when calling the `plot`

function with the same change of variable; but fail again

```
integral(lambda t: phi(t/h-1),t,0,pi)
TypeError: unable to convert <function <lambda> at 0x16d71f140> to a symbolic expression
```

Now I try to use another integration method with `definite_integral`

but get the same errors, only different for the "lambda" method

```
definite_integral(lambda x: phi(x/h-1),x,0,pi)
TypeError: cannot coerce arguments: no canonical coercion from <type 'function'> to Symbolic Ring
```

Is there any way around this? I really do not know what else to try...