integration floor

$\begin{aligned} I & = \int_{-5}^{100} (x - \lfloor x \rfloor \ dx \\ & = \int_{-5}^{100} \{ x \} \ dx & \small \blue{\text{where } \{\cdot \} \text{ denotes the fractional part function.}} \\ & = 105 \int_0^1 x \ dx & \small \blue{\text{See note}} \\ & = 105 \left[\frac {x^2}2\right]_0^1 \\ & = \frac {105}2 = \boxed{52.5} \end{aligned}$

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Note: In graph the fractional part function of $x$ appears as below. Therefore its integral is the area under the slanting lines $y=x$ where $x \in [0, 1)$ .