Why does the behave this particular way:
WolframAlpha["integrate integrate x times y from x=0 to 1 and from y=-1 to 1", IncludePods -> "Input", AppearanceElements -> {"Pods"},
TimeConstraint -> {60, Automatic, Automatic, Automatic},
PodStates -> {"Input__Step-by-step solution"}]
The solution is correct. Since the y-integration is symmetric by the interval and the integrant is antisymmetric, the solution is zero.
Problem remains, no steps given by the WolframAlpha function.