【答案】B 

【解析】 

\(f^\prime(x)=e^{x^{2}}\sin x,f^{\prime\prime}(x)=2xe^{x^{2}}\sin x + e^{x^{2}}\cos x\) 

\(f^\prime(0)=0,f^{\prime\prime}(0)=1\gt0\). 

\(x = 0\)是\(f(x)\)的极值点. 

\(g^\prime(x)=e^{x^{2}}\sin^{2}x + \sin2x\int_{0}^{x}e^{t^{2}}dt\)， 

\(g^{\prime\prime}(x)=e^{x^{2}}\sin2x + 2xe^{x^{2}}\sin^{2}x + \sin2xe^{x^{2}} + 2\cos2x\int_{0}^{x}e^{t^{2}}dt\) 

\(g^\prime(0)=0,\ g^{\prime\prime}(0)=0,\ g^{\prime\prime\prime}(0)\gt0\). 

\((0,0)\)是\(y = g(x)\)的拐点.