(A) Express $\int _ { 0 } ^ { x } \frac { \sin \left( t ^ { 2 } \right) } { t ^ { 2 } } d t$

Essay

(a) Express $\int _ { 0 } ^ { x } \frac { \sin \left( t ^ { 2 } \right) } { t ^ { 2 } } d t$ as a Maclaurin series.(b) Evaluate $\int _ { 0 } ^ { 03 } \frac { \sin \left( x ^ { 2 } \right) } { x ^ { 2 } } d x$ as a series.