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

Essay

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