Use the definition of the definite integral
So MVT for integrals: Let f be a continuos function on [a,b]. Then

• There is a number c1 E [a, b] such that faf = f(c)(ba).
• There is a number c2 = [a, b] such that f f = f(c2)(b− a).
If f f exists, then there is a number c = [a, b] such that f f = f(c)(b − a). Note: FTC is Not needed to prove MVT for integrals, but since FTC does not depend on MVT integrals, you can use FTC. thanks