I was wondering, how would one compute the value of

I was wondering, how would one compute the value of $$\mbox{Si}(\infty+i\infty)$$ which is the same as $$\int\limits_{0}^{\infty+i\infty}\frac{\sin t}{t} \mbox{d}t$$ where i is the imaginary unit, the principal square root of minus one.