Answer
$$\overline f \left( x \right) = \frac{3}{{14}}\left[ {{x^{7/3}} - {{\left( {x - 2} \right)}^{7/3}}} \right]$$
Work Step by Step
$$\eqalign{
& f\left( x \right) = {x^{4/3}} \cr
& {\text{The }}n{\text{ - unit moving average of a function }}f{\text{ is}} \cr
& \overline f \left( x \right) = \frac{1}{n}\int_{x - n}^x {f\left( t \right)} dt \cr
& {\text{The 2 - unit moving average of }}f\left( x \right) = {x^{4/3}}{\text{ is}} \cr
& \overline f \left( x \right) = \frac{1}{2}\int_{x - 2}^x {{t^{4/3}}} dt \cr
& \overline f \left( x \right) = \frac{1}{2}\left[ {\frac{3}{7}{t^{7/3}}} \right]_{x - 2}^x \cr
& \overline f \left( x \right) = \frac{3}{{14}}\left[ {{t^{7/3}}} \right] \cr
& \overline f \left( x \right) = \frac{3}{{14}}\left[ {{x^{7/3}} - {{\left( {x - 2} \right)}^{7/3}}} \right] \cr} $$
