Delta Function Limits: Solving Integrals from 0 to 1

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with limits from 0 to 1

\int delta(x) * cos(x) dx

does this delta function integral even make sense from 0 to 1?
 
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Sort of. It's a little delicate. If you take the delta function representation to be symmetric, then it's 1/2. Otherwise it's not very well defined.
 
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