Prove that if

f

is integrable on a closed bounded interval

a,b

and

cin[a,b]

, then changing the\ value of

f

at

c

does not change the fact that

f

is integrable or the value of its integral on

[a,b]^(1)

.\

^(1)

In case this is confusing, here is an equivalent formulation of this question: suppose that

f

and

g

are two functions\ on

a,b

, and that

f(x)=g(x)

for all

xin[a,b]

except possibly for

x=c

. Then show that

f

is integrable on

a,b

if and\ only if

g

is integrable

a,b

, and that if this is the case then

\\\\int_a^b f(x)dx=\\\\int_a^b g(x)dx

.

value of f at c does not change the fact that f is integrable or the value of its integral on [a,b]1. 1 In case this is confusing, here is an equivalent formulation of this question: suppose that f and g are two functions on [a,b], and that f(x)=g(x) for all x[a,b] except possibly for x=c. Then show that f is integrable on [a,b] if and only if g is integrable [a,b], and that if this is the case then abf(x)dx=abg(x)dx