Is it possible to use the Second Fundamental Theorem of Calculus on $\displaystyle C(x)$ to find $\displaystyle C'(x)$, if

$\displaystyle C(x)=\sum_{j=1}^{n}{\bigg|N_{j}\int_{x}^{x_j}{k(s) ds}\bigg|} $,

where $\displaystyle N_j$ is some constant, and $\displaystyle k(s)$ is integrable over every interval?