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## Homework Statement

The value of ∫{[x]}dx (where {} and [] denotes the fractional part of x and greatest integer function)

1) 0

2) 1

3) 2

4)all are correct

**2. The attempt at a solution**

Since [x] is always an integer, the given function will always have a value=0. I thought that since the integral is a representation of the area of a curve, this would always have an area and therefore integral=0, but if we differentiate any constant we get 0 anyway, so all should be correct where is the flaw in my concept?