2.1.3.5 ✓ Mathematica. Time used: 0.006 (sec). Leaf size: 13

ode=D[x[t],t]==1/(1+t^2); 
ic={x[1]==0}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to \arctan (t)-\frac {\pi }{4} \end{align*}