I am taking a course on Partial Differential Equations at the moment. We were introduced to the Dirac Delta function, and were told it satisfies
$$\int^b_a \delta(x)=1$$ for $a<0<b$.
Having taken a course on real analysis, I understand how this is true for the entire real number line, but struggle to see why this would be the case over a finite interval?
Would someone be able to explain this to me. (Thank you in advance).