alleryFor $a < c < b$, the integral $\int_a^b f(x)\,dx$ equals:
A$\int_a^c f(x)\,dx - \int_c^b f(x)\,dx$
B$\int_a^c f(x)\,dx + \int_c^b f(x)\,dx$
C$\int_a^c f(x)\,dx \cdot \int_c^b f(x)\,dx$
D$\int_c^b f(x)\,dx - \int_a^c f(x)\,dx$
Answer & Solution
Correct answer: B. $\int_a^c f(x)\,dx + \int_c^b f(x)\,dx$
Property IV (additivity): the integral can be split at any interior point $c$: $\int_a^b = \int_a^c + \int_c^b$.
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