Let be a differentiable function such that and for all real

MATHEMATICS · Single correct · A Level · Mathematics · Integration · Integration

Problem

Let

G

be a differentiable function such that

G(1)=3

and

G'(x)=h(x)

for all real

x

. Which of the following expressions equals

G(5)

? (a)

3+\displaystyle\int_{5}^{1} h(t)\,dt

(b)

3+h(5)

(c)

3+\displaystyle\int_{1}^{5} h(t)\,dt

(d)

\displaystyle\int_{1}^{5} h(t)\,dt