Integrate with assumptions

ClearAll[f]
f[x_,y_,n_,m_,l_]:=Sin[(n π x)/l]*Sin[(m π y)/l];

f[x,y,n,m,1]

Integrate[f[x,y,n,m,l],{x,0,l}]

Simplify[Integrate[Sin[(n π x)/l]*Sin[(m π x)/l],{x,0,l}],Assumptions->(n∈Integers&&m∈Integers&&n!=m)]

ContourPlot[f[x,n,m,1],{n,-10,10},{m,-10,10}]