For example:

Integral(f(x), (x, 0, y), (y, 0, 1) ) is the same thing as
Integral(f(x), (y, x, 1), (x, 0, 1) )
which integrates into Integral((1-x)*f(x), (x, 0, 1))

Currently:
In [ ]: integrate(f(x), (x, 0, y), (y, 0, 1))
Out[ ]: Integral(f(x), (x, 0, y), (y, 0, 1))

In [ ]: integrate(f(x), (y, x, 1), (x, 0, 1))
Out[ ]: Integral((1 - x)*f(x), (x, 0, 1))

So, should we add code to check for this and switches variables by
altering the limits to make it the same argument?

There are some issues with this approach though. For something like
Integral(f(x), (x,y, y+1), (y, 0, 2))

to be switched around it takes

Integral(f(x), (y, 0, x), (x, 0, 1)) + Integral(f(x), (y, x-1, x), (x,
1, 2)) + Integral(f(x), (y, x-1, 2), (x, 2, 3))

because the equations defining the limits of integration change
depending on the value of x.

I was just wondering if this is something to consider. Would it even
be very useful? Am I doing this correctly?

Also, still a little new here so any pointers on how to do things and/
or advice on what I'm doing wrong would be very much appreciated.

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