Mathematics

Problem

Let

f

be a continuous function on

[-2,5]

such that

f(x)>0

for

-2<x<1

and

f(x)<0

for

1<x<5

with

f(1)=0

. State whether the definite integral

\displaystyle\int_{-2}^{5} f(x)\,dx

must be (i) positive, (ii) negative, or (iii) may be zero. Give your answer and one‐line reason.