Paneer Definite Masala 1

$\begin{aligned}\displaystyle \int\limits_0^{100} \left \lfloor \tan^{-1} x\right \rfloor \mathrm{d}x&=\int\limits_0^{\tan 1} \left \lfloor \tan^{-1} x\right \rfloor \mathrm{d}x + \int\limits_{\tan 1}^{100} \left \lfloor \tan^{-1} x\right \rfloor \mathrm{d}x \\&=\int\limits_0^{\tan 1} 0 \mathrm{d}x + \int\limits_{\tan 1}^{100} 1 \mathrm{d}x\\ &= 100 - \tan 1\\&\approx 98.44259\end{aligned}\\\huge \boxed{\displaystyle\int\limits_0^{100} \left \lfloor \tan^{-1} x\right \rfloor \mathrm{d}x = 100 - \tan 1^c}$