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decomposition of definite integral

see definite integral

for intervals [a,c]=[a,b]∪[b,c],

∫acf(x)dx=∫abf(x)dx+∫bcf(x)dx

PROOF/

By the Fundamental Theorem of Calculus,

∫acf(x)dx=F(c)−F(a)

and

∫abf(x)dx+∫bcf(x)dx=(F(b)−F(a))+(F(c)−F(b))=F(c)−F(a)=∫acf(x)dx

QED

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