Let X(jω) be the Fourier transform of x(t), with $X(j\omega)=10e^{-j\pi f}\sin(\pi f)/(\pi f)$ and ω=2πf. Evaluate $\frac1{2\pi}\int_{-\infty}^{\infty}X(j\omega)\,d\omega$.
The spectrum is that of a height-ten unit-width rectangle centered at t=.5, supported from zero to one. The inverse-transform integral at the jump t=0 yields the midpoint value five under the usual symmetric Fourier inversion convention. The official C gives ten by assigning the rectangle its inside endpoint value at zero. The source omits an endpoint convention, so its grading C is preserved while the jump-value issue is explicit.
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