lf f(x) is continuous for all real values of x, then ∑n=110 ∫01 f(r−1+x)dx

I=∑r=110 ∫01 f(r−1+x)dxIt=∫01 f(t−1+x)dx Put t−1+x=y⇒dx=dy It=∫t−1t f(y)dy⇒It=∫t−1t f(x)dxI1=∫01 f(x)dx,I2=∫12 f(x)dx I3=∫23 f(x)dxr...I10=∫910 f(x)dx I = I1+I2+....+I10=∫01 f(x)dx+∫12 f(x)dx+........+∫910 f(x)dx=∫010 f(x)dx