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Why is

[.] denotes the greatest integer function. Is it because

Similarly, how can we substitute

**?**_{π/2}∫^{3π/2}[cos^{-1}t].dt =_{π/2}∫^{3π/2}-1.dt[.] denotes the greatest integer function. Is it because

**[cos**= -1 in t ∈ [π/2,3π/2)? But^{-1}t]**[cos**= 0 for x = 3π/2. So we have one 0 along with all the -1's in (π/2,3π/2]. So how can we substitute^{-1}t]**[cos**= -1 for every x in (π/2,3π/2] even though^{-1}t]**[cos**= 0 at x = 3π/2?^{-1}t]Similarly, how can we substitute

**even though**_{3π/2}∫^{2π}[cos^{-1}t].dt =_{3π/2}∫^{2π}0.dt**[cos**= 1 at x = 2π?^{-1}t]
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