By the Second Fundamental Theorem of Calculus, if $F'=f$ on $[a,b]$, then $\int_a^b f(x)\,dx$ equals
A$F(a)-F(b)$
B$F(b)-F(a)$
C$F(b)+F(a)$
D$F'(b)-F'(a)$
Answer & Solution
Correct answer: B. $F(b)-F(a)$
1. The theorem states $\int_a^b f(x)\,dx=[F(x)]_a^b$.
2. This means upper-limit value minus lower-limit value.
3. Hence $\int_a^b f(x)\,dx=F(b)-F(a)$.
_Source: NCERT Class 12 Mathematics Ch 7 "Integrals", p.334_
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