# Test your Skill Ceiling in Integration

Calculus Level 4

$\large \int _{ 0 }^{ 2 }{ \lceil x \rceil \, d \lfloor x \rfloor }$

Evaluate the Riemann-Stieltjes integral above, using the definition given in the link.

Enter 666 if you come to the conclusion that this integral fails to exist. 

Bonus What if we use the definition of the Riemann-Stieltjes integral found here (Definition 6.7.2)

Notations: $$\lfloor \cdot \rfloor$$ denotes the floor function and $$\lceil \cdot \rceil$$ denotes the ceiling function.

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