A continuous random variable X that can assume values betweenxequals1andxequals4has a density function given byf(x)equalsone third.(a) Show that the area under the curve is equal to 1.(b) FindP(3less thanXless than3.1).(c) FindP(Xless than or equals1.8).Question content area bottomPart 1(a) Which of the following definite integrals shows that the area under the given curve is1? Select the correct choice below and fill in the answer box to complete your choice.A.Integral from 1 to 4 left parenthesis one third right parenthesis dx equals nothing vertical line Subscript 1 Superscript 4 Baseline equals 1Integral from 1 to 4 left parenthesis one third right parenthesis dx equals nothing vertical line Subscript 1 Superscript 4 Baseline equals 1B.Integral from 1 to 1 left parenthesis one third right parenthesis dx equals nothing vertical line Subscript 1 Superscript 1 Baseline equals 1Integral from 1 to 1 left parenthesis one third right parenthesis dx equals nothing vertical line Subscript 1 Superscript 1 Baseline equals 1C.Integral from 3 to 4 left parenthesis one third right parenthesis dx equals nothing vertical line Subscript 3 Superscript 4 Baseline equals 1Integral from 3 to 4 left parenthesis one third right parenthesis dx equals nothing vertical line Subscript 3 Superscript 4 Baseline equals 1D.Integral from negative infinity to infinity left parenthesis one third right parenthesis dx equals nothing vertical line Subscript infinity Superscript infinity Baseline equals 1Integral from negative infinity to infinity left parenthesis one third right parenthesis dx equals nothing vertical line Subscript infinity Superscript infinity Baseline equals 1Part 2(b)P(3less thanXless than3.1)equalsenter your response here(Simplify your answer.)Part 3(c)P(Xless than or equals1.8)equalsenter your response here(Simplify your answer.)