Concept:The remainder is found by polynomial long division: divide leading terms, multiply, subtract, and repeat until the remainder has a lower degree than the divisor.Explanation:Divide X3 by X2 to get X.Multiply: X(X2+1)=X3+X.Subtract: (X3−2X2+3X−3)−(X3+X)=−2X2+2X−3.Divide −2X2 by X2 to get −2.Multiply: −2(X2+1)=−2X2−2.Subtract: (−2X2+2X−3)−(−2X2−2)=2X−1.The degree of 2X−1 is 1, which is less than the degree of X2+1, so the division stops.Answer:Remainder =2X−1, so the correct option is A.