Antiderivatives and definite integrals

Compute the following integral:

$I={\int}_{0}^{1}{\textstyle (}{\int}_{1}^{x}\frac{1}{1+{t}^{2}}dt{\textstyle )}dx$

Motivation: From time to time, i intend to post here challenging questions -together with proposed answers/solutions- which i frequently give for practise to some of my students (in an introductory calculus course).

I am doing this with the understanding that this is not only accepted but furthermore encouraged by the community. The benefits can be twofold: on the one hand this contributes to building a library with well-posed questions and reliable answers (to be used in-class or online) and on the other hand i always hope that this may result in improving (or sometimes correcting) the proposed questions/answers and discovering new approaches/solutions from other users as well.

Compute the following integral:

$I={\int}_{0}^{1}{\textstyle (}{\int}_{1}^{x}\frac{1}{1+{t}^{2}}dt{\textstyle )}dx$

Motivation: From time to time, i intend to post here challenging questions -together with proposed answers/solutions- which i frequently give for practise to some of my students (in an introductory calculus course).

I am doing this with the understanding that this is not only accepted but furthermore encouraged by the community. The benefits can be twofold: on the one hand this contributes to building a library with well-posed questions and reliable answers (to be used in-class or online) and on the other hand i always hope that this may result in improving (or sometimes correcting) the proposed questions/answers and discovering new approaches/solutions from other users as well.