The standard Dirichlet integral is $\int_{-\infty}^{\infty}\sin(at)/t\,dt=\pi$ for a>0, interpreted as the symmetric improper integral.
With a=2π, dividing by π gives one. The prefactor two therefore makes the requested value **2, D**. The removable value at t=0 does not affect the integral.
More Calculus: Mean value theorems, Theorems of integral calculus, Evaluation of definite and improper integrals, Partial derivatives, Multiple integrals, Fourier series questions
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