Dirac delta function and dirac measure

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I want to know the relationship between these two things. e.g. What's the results of following integrals? (Let $\mu$ Lebesgue measure, $\nu$ Dirac measure) $$(1)\int\delta_c(x)\mu(dx)$$ $$(2)\int\delta_c(x)\nu(dx)$$ $$(3)\int f(x)\delta_c(x)\mu(dx)$$ $$(4)\int f(x)\delta_c(x)\nu(dx)$$