normalizedfplot={{0.01, 0.}, {0.02, -0.0000442749}, {0.03, -0.0000825681}, {0.04,
-0.000118506}, {0.05, -0.000153786}, {0.06, -0.000189389}, {0.07,
-0.000225942}, {0.08, -0.000263877}, {0.09, -0.000303499}, {0.1,
-0.000345031}, {0.11, -0.000388637}, {0.12, -0.000434434}, {0.13,
-0.000482508}, {0.14, -0.000532918}, {0.15, -0.000585696}, {0.16,
-0.00064086}, {0.17, -0.000698408}, {0.18, -0.000758323}, {0.19,
-0.000820576}, {0.2, -0.000885121}, {0.21, -0.000951904}, {0.22,
-0.00102085}, {0.23, -0.00109189}, {0.24, -0.00116491}, {0.25,
-0.00123982}, {0.26, -0.00131648}, {0.27, -0.00139477}, {0.28,
-0.00147452}, {0.29, -0.00155556}, {0.3, -0.0016377}, {0.31,
-0.00172073}, {0.32, -0.00180441}, {0.33, -0.00188848}, {0.34,
-0.00197263}, {0.35, -0.00205655}, {0.36, -0.00213987}, {0.37,
-0.00222218}, {0.38, -0.00230301}, {0.39, -0.00238187}, {0.4,
-0.00245817}, {0.41, -0.00253126}, {0.42, -0.00260043}, {0.43,
-0.00266488}, {0.44, -0.00272373}, {0.45, -0.00277602}, {0.46,
-0.00282075}, {0.47, -0.00285692}, {0.48, -0.00288357}, {0.49,
-0.00289991}, {0.5, -0.00290542}, {0.51, -0.00289991}, {0.52,
-0.00288357}, {0.53, -0.00285692}, {0.54, -0.00282075}, {0.55,
-0.00277602}, {0.56, -0.00272373}, {0.57, -0.00266488}, {0.58,
-0.00260043}, {0.59, -0.00253126}, {0.6, -0.00245817}, {0.61,
-0.00238187}, {0.62, -0.00230301}, {0.63, -0.00222218}, {0.64,
-0.00213987}, {0.65, -0.00205655}, {0.66, -0.00197263}, {0.67,
-0.00188848}, {0.68, -0.00180441}, {0.69, -0.00172073}, {0.7,
-0.0016377}, {0.71, -0.00155556}, {0.72, -0.00147452}, {0.73,
-0.00139477}, {0.74, -0.00131648}, {0.75, -0.00123982}, {0.76,
-0.00116491}, {0.77, -0.00109189}, {0.78, -0.00102085}, {0.79,
-0.000951904}, {0.8, -0.000885121}, {0.81, -0.000820576}, {0.82,
-0.000758323}, {0.83, -0.000698408}, {0.84, -0.00064086}, {0.85,
-0.000585696}, {0.86, -0.000532918}, {0.87, -0.000482508}, {0.88,
-0.000434434}, {0.89, -0.000388637}, {0.9, -0.000345031}, {0.91,
-0.000303499}, {0.92, -0.000263877}, {0.93, -0.000225942}, {0.94,
-0.000189389}, {0.95, -0.000153786}, {0.96, -0.000118506}, {0.97,
-0.0000825681}, {0.98, -0.0000442749}, {0.99, 0.}}

fo = Interpolation[normalizedfplot, Method -> "Spline"];
 boundary = FindRoot[{y1==fo[x1],y2==fo[x2], fo'[x1]==fo'[x2], fo'[x1]==(y2-y1)/(x2-x1)},
  {x1,0.01},{x2,0.5},{y1,-0.025},{y2,-0.0275}]

{x1 -> -0.00170598, x2 -> 0.427377, y1 -> 0.0000649291,
 y2 -> -0.00264848}