Let be a real interval line $[a,b]$ and define the continuos function $f:[a,b]\rightarrow\mathbb{R}$. If split this interval in $\left\{{t _k, k=1,...,L+1}\right\}$ where $t_1=a$ and $t_{L+1}=b$. I will be able to say
$\int_a^bf(x)dx=\sum_{k=1}^{L+1}\int_{t_k}^{t_{k+1}}f(x)dx?$