i get a different result

pprint(Integral((sin(m*pi*x/a)*sin(pi*x/a)), (x,0,a)).doit() )
        2                     2  2
     a⋅π ⋅sin(π⋅m)         a⋅π ⋅m ⋅sin(π⋅m)
- ──────────────────── + ────────────────────
     3  2    3    3  4      3  2    3    3  4
  2⋅π ⋅m  - π  - π ⋅m    2⋅π ⋅m  - π  - π ⋅m

but my error is that i forgot to express that i am assuming m is an
integer. although i have not set this flag because the integral
evaluates incorrectly ( you actually helped me with this about year
ago)

so maybe the intuitive answer i am looking for is a correct evaluation
of the integral when m.is_integer is true.

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