Question content area topPart 1A continuous random variable X that can assume values betweenxequals3andxequals6has a density function given byf(x)equalsone third.(a) Show that the area under the curve is equal to 1.(b) FindP(5less thanXless than5.3).(c) FindP(Xless than or equals3.4).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 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 1B.Integral from 3 to 6 left parenthesis one third right parenthesis dx equals nothing vertical line Subscript 3 Superscript 6 Baseline equals 1Integral from 3 to 6 left parenthesis one third right parenthesis dx equals nothing vertical line Subscript 3 Superscript 6 Baseline equals 1C.Integral from 5 to 6 left parenthesis one third right parenthesis dx equals nothing vertical line Subscript 5 Superscript 6 Baseline equals 1Integral from 5 to 6 left parenthesis one third right parenthesis dx equals nothing vertical line Subscript 5 Superscript 6 Baseline equals 1D.Integral from 3 to 3 left parenthesis one third right parenthesis dx equals nothing vertical line Subscript 3 Superscript 3 Baseline equals 1Integral from 3 to 3 left parenthesis one third right parenthesis dx equals nothing vertical line Subscript 3 Superscript 3 Baseline equals 1Part 2(b)P(5less thanXless than5.3)equalsenter your response here(Simplify your answer.)Part 3(c)P(Xless than or equals3.4)equalsenter your response here(Simplify your answer.)