f(x)=

\int_{a}^{b}{ }{f(x)}dx=\int_{a}^{c}{ }{f(x)}dx+\int_{c}^{b}{ }{f(x)}dx \;  \;  \; where  \;  \; a  <c<b

Property \; of  \; Definite \; Integrals

ROHIT SINGH (KVS)
CC BY SA

f(x) = (0.2 * x) + 1
a = -1 (slider from -5 to 10, step 1)
b = 3 (slider from -5 to 10, step 1)
d = Integral(f(x), a, b)
eq1: x = a
eq2: x = b
A = Intersect(xAxis, eq1)
B = Intersect(xAxis, eq2)
D = Intersect(d, f, 1)
InputBox1 = Textfield(f)
c = 3 (slider from a to b, step 1)
eq3: x = c
C = Intersect(xAxis, eq3)
E = Intersect(f, eq3)
g = Segment(E, C)
e = Integral(f(x), a, c)
h = Integral(f(x), c, b)
p = Integral(f(x), x)
i: p(a)
j: p(b)
k: p(c)
text1: "\int_{" + (LaTeX[a]) + "}^{" + (LaTeX[b]) + "}{ }(" + (LaTeX[f]) + ")dx=\int_{" + (LaTeX[a]) + "}^{" + (LaTeX[c]) + "}{ }(" + (LaTeX[f]) + ")dx+\int_{" + (LaTeX[c]) + "}^{" + (LaTeX[b]) + "}{ }(" + (LaTeX[f]) + ")dx"
text3: "[" + (LaTeX[p]) + "]_{" + (LaTeX[a]) + "}^{" + (LaTeX[b]) + "}=[" + (LaTeX[p]) + "]_{" + (LaTeX[a]) + "}^{" + (LaTeX[c]) + "} \; +[" + (LaTeX[p]) + "]_{" + (LaTeX[c]) + "}^{" + (LaTeX[b]) + "}"
text4: "(" + (LaTeX[i]) + ")-(" + (LaTeX[j]) + ")=[(" + (LaTeX[i]) + ")-(" + (LaTeX[k]) + ")]+[(" + (LaTeX[k]) + ")-(" + (LaTeX[j]) + ")]"
text6: "" + (LaTeX[d]) + "=" + (LaTeX[d]) + ""
c_{1} = 0
text5: "" + (LaTeX[d]) + "=(" + (LaTeX[e]) + ") \; + \;( " + (LaTeX[h]) + ")"