restart;with( Student[Calculus1] );f := x/(x^4+1);A := 0;B := 4;N := 4;ApproximateInt(f, A..B, partition = N, method = left, output = sum);ApproximateInt(f, A..B, partition = N, method = left, output = plot);ApproximateInt(f, A..B, partition = N, method = midpoint, output = sum);ApproximateInt(f, A..B, partition = N, method = midpoint, output = plot);ApproximateInt(f, A..B, partition = N, method = right, output = sum);ApproximateInt(f, A..B, partition = N, method = right, output = plot);ApproximateInt(f, A..B, partition = N, output = animation);ApproximateInt(f, A..B, partition = n, method = left, output = sum);limit( %, n=infinity );evalf( % );q1 := ApproximateInt(f, a..b, partition = n, method = left, output = sum);#value( % );#simplify( %, n );#collect( %, n );q2 := limit( q1, n=infinity );F := int( f, x );q3 := eval( F, x=b ) - eval( F, x=a );q4 := int( f, x=a..b );