Good evening everybody,
the appended file shows an irritating (at least for me) behavior.
Simplifying the integral of the title under the assumption that m and n are integers one gets 0.
This is obviously wrong for m==n ! Is there a reason?
Thank you, Gentlemen
for the fast and insightful response. Particularly that of Illian made me better prepared for similar situations.
Also, your sol2 seems to use the assumptions after the actual integration. This seems to work better:
Integrate[Sin[n*Pi*x]*Sin[m*Pi*x], {x, 0, 1}, Assumptions -> {m \[Element] Integers, n \[Element] Integers, m == n}]
There is some discussion of this topic in the documentation
http://reference.wolfram.com/language/tutorial/GenericAndNonGenericCases.html
