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Bug in NIntegrate[]?


I define the function f[x] as follows:

f[x_] := 0 /; x < 0 || x > 1;
f[x_] := 1

It is zero outside of the interval [0,1]. This can be verified by plotting
Plot[f[x], {x, -1, 2}]

Now I integrate it from -1 to 2:
In[270]:= NIntegrate[f[x], {x, -1, 2}]
Out[270]= 3.

The result should be 1, but it is 3. Clearly Mathematica ignores the fact that f[x] is zero outside of [0,1].

This caused a lot of headache for me recently when I encountered such behavior in one of my research code.
GS 



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