add definite integral interface for polyint

Author: jverzani

src/Polynomials.jl

@@ -430,6 +430,7 @@ polyval(p::Poly, v::AbstractArray) = map(x->polyval(p, x), v)
 @compat (p::Poly)(x) = polyval(p, x)
 
 """
+Indefinite integral of a polynomial.
 
 * `polyint(p::Poly, k::Number=0)`: Integrate the polynomial `p` term
   by term, optionally adding constant term `k`. The order of the
@@ -441,6 +442,7 @@ polyint(Poly([1, 0, -1]))     # Poly(x - 0.3333333333333333x^3)
 polyint(Poly([1, 0, -1]), 2)  # Poly(2.0 + x - 0.3333333333333333x^3)
 ```
 
+See also `polyint(p, a, b)` for a definite integral over `[a,b]`.
 """
 # if we do not have any initial condition, assume k = zero(Int)
 polyint{T}(p::Poly{T}) = polyint(p, 0)
@@ -479,6 +481,22 @@ end
 
 """
 
+* `polyint(p::Poly, a::Number, b::Number)`: Definite integral of the polynomial `p` over the interval `[a,b]`.
+
+Examples:
+```
+x = variable()
+p = 1 - x^2
+polyint(p, 0, 1)
+```
+"""
+function polyint(p::Poly, a::Number, b::Number)
+    P = polyint(p)
+    P(b) - P(a)
+end
+
+"""
+
 * `polyder(p::Poly)`: Differentiate the polynomial `p` term by
   term. The order of the resulting polynomial is one lower than the
   order of `p`.

test/runtests.jl

@@ -51,11 +51,13 @@ sprint(show, pNULL)
 @test polyval(poly([1//2, 3//2]), 1//2) == 0//1
 @test polyder(polyint(pN)) == pN
 @test polyder(pR) == Poly([-2//1,2//1])
+@test polyder(p3) == Poly([2,2])
+@test polyder(p1) == polyder(p0) == polyder(pNULL) == pNULL
 @test_throws ErrorException polyder(pR, -1)
 @test polyint(pNULL,1) == p1
 @test polyint(Poly(Rational[1,2,3])) == Poly(Rational[0, 1, 1, 1])
-@test polyder(p3) == Poly([2,2])
-@test polyder(p1) == polyder(p0) == polyder(pNULL) == pNULL
+@test polyint(p2, 0, 2) == 4.0
+
 
 @test pN(-.125) == 276.9609375
 @test pN([0.1, 0.2, 0.3]) == polyval(pN, [0.1, 0.2, 0.3])