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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

$\int_a^bf(x)dx=\sum_{k=1}^{L+1}\int_{t_k}^{t_{k+1}}f(x)dx?$

1 Answers 1

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Almost. You want the last interval to be $[t_L,t_{L+1}]$, not $[t_{L+1},t_{L+2}]$.

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